home *** CD-ROM | disk | FTP | other *** search
| Unknown | 1996-09-28 | 29.7 KB | [FRO2/BTWS] |
open in: 
MacOS 8.1
|
Win98
|
DOS
view JSON data
|
view as text
This file was not able to be converted.
This format is not currently supported by dexvert.
| Confidence | Program | Detection | Match Type | Support
|
|---|
| 100%
| file
| data
| default
| |
| 100%
| TrID
| Adobe PhotoShop Brush
| default (weak)
|
|
| id metadata |
|---|
| key | value |
|---|
| macFileType | [FRO2] |
| macFileCreator | [BTWS] |
hex view+--------+-------------------------+-------------------------+--------+--------+
|00000000| 00 00 00 0a 00 25 00 00 | 01 51 02 12 00 00 00 01 |.....%..|.Q......|
|00000010| 00 01 00 02 00 00 00 88 | 00 01 00 03 00 03 00 09 |........|........|
|00000020| 00 00 11 95 00 03 00 0a | 00 03 00 1b 00 00 15 30 |........|.......0|
|00000030| 00 03 00 1c 00 04 00 08 | 00 00 15 30 00 04 00 09 |........|...0....|
|00000040| 00 04 00 1a 00 00 1f 3f | 00 04 00 1b 00 04 00 2b |.......?|.......+|
|00000050| 00 00 1f 3f 00 04 00 2c | 00 04 00 00 00 00 1f 3f |...?...,|.......?|
|00000060| 00 05 00 01 00 05 00 00 | 00 00 2f b4 00 06 00 01 |........|../.....|
|00000070| 00 06 00 12 00 00 6d 64 | 00 06 00 13 00 07 00 00 |......md|........|
|00000080| 00 00 6d 64 00 00 00 08 | 00 00 00 01 00 00 10 f7 |..md....|........|
|00000090| 00 00 00 00 00 8f fe 48 | 00 8f fe b8 01 00 10 f7 |.......H|........|
|000000a0| 00 0a 00 00 01 13 01 82 | 11 01 a1 00 64 00 0a 46 |........|....d..F|
|000000b0| 57 52 54 00 0b 01 1b 01 | 82 a1 00 64 00 38 46 57 |WRT.....|...d.8FW|
|000000c0| 52 54 00 01 07 1b 00 00 | 00 01 00 00 00 00 00 00 |RT......|........|
|000000d0| 00 00 ff ff ff ff ff ff | ff ff 00 02 00 08 00 00 |........|........|
|000000e0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 8e |........|........|
|000000f0| ff fd 00 8e 01 71 01 00 | 0a 00 0a 00 00 01 13 01 |.....q..|........|
|00000100| 82 20 00 8e ff fd 00 8e | 01 71 a1 00 64 00 38 46 |. ......|.q..d.8F|
|00000110| 57 52 54 00 01 07 1b 00 | 00 00 01 00 00 00 00 00 |WRT.....|........|
|00000120| 00 00 00 ff ff ff ff ff | ff ff ff 00 02 00 08 00 |........|........|
|00000130| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000140| 1f 00 54 00 8f 00 27 22 | 00 1f 00 54 d3 70 a1 00 |..T...'"|...T.p..|
|00000150| 64 00 38 46 57 52 54 00 | 01 07 1b 00 00 00 01 00 |d.8FWRT.|........|
|00000160| 00 00 00 00 00 00 00 ff | ff ff ff ff ff ff ff 00 |........|........|
|00000170| 02 00 08 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000180| 00 00 00 00 1e 00 54 00 | 8e 00 63 22 00 1e 00 54 |......T.|..c"...T|
|00000190| 0f 70 a1 00 64 00 38 46 | 57 52 54 00 01 07 1b 00 |.p..d.8F|WRT.....|
|000001a0| 00 00 01 00 00 00 00 00 | 00 00 00 ff ff ff ff ff |........|........|
|000001b0| ff ff ff 00 02 00 08 00 | 00 00 00 00 00 00 00 00 |........|........|
|000001c0| 00 00 00 00 00 00 00 00 | 1e 00 54 00 8f 00 ac 22 |........|..T...."|
|000001d0| 00 1e 00 54 58 71 a1 00 | 64 00 38 46 57 52 54 00 |...TXq..|d.8FWRT.|
|000001e0| 01 07 1b 00 00 00 01 00 | 00 00 00 00 00 00 00 ff |........|........|
|000001f0| ff ff ff ff ff ff ff 00 | 02 00 08 00 00 00 00 00 |........|........|
|00000200| 00 00 00 00 00 00 00 00 | 00 00 00 00 1f 00 55 00 |........|......U.|
|00000210| 90 01 67 20 00 1f 00 55 | 00 90 01 67 a1 00 64 00 |..g ...U|...g..d.|
|00000220| 38 46 57 52 54 00 01 07 | 1b 00 00 00 01 00 00 00 |8FWRT...|........|
|00000230| 00 00 00 00 00 ff ff ff | ff ff ff ff ff 00 02 00 |........|........|
|00000240| 08 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000250| 00 00 8d 00 87 00 a9 00 | 87 22 00 8d 00 87 00 1c |........|."......|
|00000260| a1 00 64 00 38 46 57 52 | 54 00 01 07 1b 00 00 00 |..d.8FWR|T.......|
|00000270| 01 00 00 00 00 00 00 00 | 00 ff ff ff ff ff ff ff |........|........|
|00000280| ff 00 02 00 08 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000290| 00 00 00 00 00 00 8e 00 | b5 01 0b 00 b5 22 00 8e |........|....."..|
|000002a0| 00 b5 00 7d a1 00 64 00 | 38 46 57 52 54 00 01 07 |...}..d.|8FWRT...|
|000002b0| 1b 00 00 00 01 00 00 00 | 00 00 00 00 00 ff ff ff |........|........|
|000002c0| ff ff ff ff ff 00 02 00 | 08 00 00 00 00 00 00 00 |........|........|
|000002d0| 00 00 00 00 00 00 00 00 | 00 00 20 00 55 01 0d 00 |........|.. .U...|
|000002e0| b5 20 00 20 00 55 01 0d | 00 b5 a1 00 64 00 38 46 |. . .U..|....d.8F|
|000002f0| 57 52 54 00 01 03 1b 00 | 11 00 00 00 00 00 00 00 |WRT.....|........|
|00000300| 00 00 00 ff ff ff ff ff | ff ff ff 00 00 00 08 00 |........|........|
|00000310| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000320| 0c 00 0e 00 1b 00 18 09 | 00 00 00 00 00 00 00 00 |........|........|
|00000330| 31 00 0c 00 0e 00 1b 00 | 18 a1 00 64 00 78 46 57 |1.......|...d.xFW|
|00000340| 52 54 00 01 01 c4 00 11 | 00 01 00 00 00 00 00 00 |RT......|........|
|00000350| 00 00 ff ff ff ff ff ff | ff ff 00 02 00 01 00 00 |........|........|
|00000360| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 19 |........|........|
|00000370| 00 46 00 26 00 6d 00 19 | 00 46 00 19 00 6c 00 00 |.F.&.m..|.F...l..|
|00000380| 00 01 00 00 00 0c 00 14 | 01 00 00 00 40 00 00 00 |........|....@...|
|00000390| 00 00 01 00 00 00 00 01 | 00 00 00 0c 00 14 01 00 |........|........|
|000003a0| 00 00 00 00 00 00 ff ff | ff ff ff ff ff ff ff ff |........|........|
|000003b0| 00 04 00 00 50 a4 90 00 | 06 00 00 00 00 00 0d 00 |....P...|........|
|000003c0| 27 00 00 00 00 00 0d 00 | 27 00 19 00 46 00 26 00 |'.......|'...F.&.|
|000003d0| 6d 00 01 00 00 00 00 00 | 00 3e 00 00 00 00 00 11 |m.......|.>......|
|000003e0| 00 00 00 00 00 11 00 00 | 00 00 00 11 00 00 00 00 |........|........|
|000003f0| 00 1e 00 00 00 00 00 10 | 00 00 00 00 00 10 00 00 |........|........|
|00000400| 00 00 00 38 00 00 00 00 | 00 00 00 00 00 00 00 00 |...8....|........|
|00000410| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000420| 00 a1 00 64 00 38 46 57 | 52 54 00 01 03 c4 00 00 |...d.8FW|RT......|
|00000430| 00 01 00 00 00 00 00 00 | 00 00 ff ff ff ff ff ff |........|........|
|00000440| ff ff 00 00 00 08 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000450| 00 00 00 00 00 00 00 14 | 00 45 00 23 00 4f a1 00 |........|.E.#.O..|
|00000460| 64 00 38 46 57 52 54 00 | 01 03 c4 00 11 00 00 00 |d.8FWRT.|........|
|00000470| 00 00 00 00 00 00 00 ff | ff ff ff ff ff ff ff 00 |........|........|
|00000480| 00 00 08 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000490| 00 00 00 00 92 00 22 00 | a1 00 2d 31 00 92 00 22 |......".|..-1..."|
|000004a0| 00 a1 00 2d a1 00 64 00 | 78 46 57 52 54 00 01 01 |...-..d.|xFWRT...|
|000004b0| 00 00 11 00 01 00 00 00 | 00 00 00 00 00 ff ff ff |........|........|
|000004c0| ff ff ff ff ff 00 02 00 | 01 00 00 00 00 00 00 00 |........|........|
|000004d0| 00 00 00 00 00 00 00 00 | 00 00 92 00 23 00 9f 00 |........|....#...|
|000004e0| 4a 00 92 00 23 00 92 00 | 49 00 00 00 01 00 00 00 |J...#...|I.......|
|000004f0| 0c 00 14 01 00 00 00 40 | 00 00 00 00 00 01 00 00 |.......@|........|
|00000500| 00 00 01 00 00 00 0c 00 | 14 01 00 00 00 00 00 00 |........|........|
|00000510| 00 ff ff ff ff ff ff ff | ff ff ff 00 04 00 00 41 |........|.......A|
|00000520| a4 90 00 06 00 00 00 00 | 00 0d 00 27 00 00 00 00 |........|...'....|
|00000530| 00 0d 00 27 00 92 00 23 | 00 9f 00 4a 00 01 00 00 |...'...#|...J....|
|00000540| 00 00 00 00 04 00 00 00 | 00 00 04 00 00 00 00 00 |........|........|
|00000550| 0a 00 00 00 00 00 0a 00 | 00 00 00 00 11 00 00 00 |........|........|
|00000560| 00 00 1f 00 00 00 00 00 | 20 80 00 00 00 00 31 c0 |........| .....1.|
|00000570| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000580| 00 00 00 00 00 00 00 00 | 00 00 00 00 a1 00 64 00 |........|......d.|
|00000590| 38 46 57 52 54 00 01 03 | 00 00 00 00 01 00 00 00 |8FWRT...|........|
|000005a0| 00 00 00 00 00 ff ff ff | ff ff ff ff ff 00 00 00 |........|........|
|000005b0| 08 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|000005c0| 00 00 92 00 22 00 a1 00 | 2d a1 00 64 00 38 46 57 |...."...|-..d.8FW|
|000005d0| 52 54 00 01 03 00 00 11 | 00 00 00 00 00 00 00 00 |RT......|........|
|000005e0| 00 00 ff ff ff ff ff ff | ff ff 00 00 00 08 00 00 |........|........|
|000005f0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 92 |........|........|
|00000600| 00 5d 00 a1 00 68 31 00 | 92 00 5d 00 a1 00 68 a1 |.]...h1.|..]...h.|
|00000610| 00 64 00 78 46 57 52 54 | 00 01 01 c4 00 11 00 01 |.d.xFWRT|........|
|00000620| 00 00 00 00 00 00 00 00 | ff ff ff ff ff ff ff ff |........|........|
|00000630| 00 02 00 01 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000640| 00 00 00 00 00 92 00 5e | 00 9f 00 85 00 92 00 5e |.......^|.......^|
|00000650| 00 92 00 84 00 00 00 01 | 00 00 00 0c 00 14 01 00 |........|........|
|00000660| 00 00 40 00 00 00 00 00 | 01 00 00 00 00 01 00 00 |..@.....|........|
|00000670| 00 0c 00 14 01 00 00 00 | 00 00 00 00 ff ff ff ff |........|........|
|00000680| ff ff ff ff ff ff 00 04 | 00 00 42 a4 90 00 06 00 |........|..B.....|
|00000690| 00 00 00 00 0d 00 27 00 | 00 00 00 00 0d 00 27 00 |......'.|......'.|
|000006a0| 92 00 5e 00 9f 00 85 00 | 01 00 00 00 00 00 00 3e |..^.....|.......>|
|000006b0| 00 00 00 00 00 11 00 00 | 00 00 00 11 00 00 00 00 |........|........|
|000006c0| 00 1e 00 00 00 00 00 11 | 00 00 00 00 00 11 00 00 |........|........|
|000006d0| 00 00 00 11 00 00 00 00 | 00 3e 00 00 00 00 00 00 |........|.>......|
|000006e0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|000006f0| 00 00 00 00 00 00 00 a1 | 00 64 00 38 46 57 52 54 |........|.d.8FWRT|
|00000700| 00 01 03 f4 00 00 00 01 | 00 00 00 00 00 00 00 00 |........|........|
|00000710| ff ff ff ff ff ff ff ff | 00 00 00 08 00 00 00 00 |........|........|
|00000720| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 92 00 5d |........|.......]|
|00000730| 00 a1 00 68 a1 00 64 00 | 38 46 57 52 54 00 01 03 |...h..d.|8FWRT...|
|00000740| f4 00 11 00 00 00 00 00 | 00 00 00 00 00 ff ff ff |........|........|
|00000750| ff ff ff ff ff 00 00 00 | 08 00 00 00 00 00 00 00 |........|........|
|00000760| 00 00 00 00 00 00 00 00 | 00 00 7c 00 aa 00 8b 00 |........|..|.....|
|00000770| b5 31 00 7c 00 aa 00 8b | 00 b5 a1 00 64 00 78 46 |.1.|....|....d.xF|
|00000780| 57 52 54 00 01 01 f4 00 | 11 00 01 00 00 00 00 00 |WRT.....|........|
|00000790| 00 00 00 ff ff ff ff ff | ff ff ff 00 02 00 01 00 |........|........|
|000007a0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|000007b0| 80 00 a6 00 8d 00 cd 00 | 80 00 a6 00 80 00 cc 00 |........|........|
|000007c0| 00 00 01 00 00 00 0c 00 | 14 01 00 00 00 40 00 00 |........|.....@..|
|000007d0| 00 00 00 01 00 00 00 00 | 01 00 00 00 0c 00 14 01 |........|........|
|000007e0| 00 00 00 00 00 00 00 ff | ff ff ff ff ff ff ff ff |........|........|
|000007f0| ff 00 04 00 00 43 a4 90 | 00 06 00 00 00 00 00 0d |.....C..|........|
|00000800| 00 27 00 00 00 00 00 0d | 00 27 00 80 00 a6 00 8d |.'......|.'......|
|00000810| 00 cd 00 01 00 00 00 00 | 00 00 0e 80 00 00 00 00 |........|........|
|00000820| 11 80 00 00 00 00 20 80 | 00 00 00 00 20 00 00 00 |...... .|.... ...|
|00000830| 00 00 20 00 00 00 00 00 | 20 80 00 00 00 00 11 00 |.. .....| .......|
|00000840| 00 00 00 00 0e 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000850| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000860| 00 00 a1 00 64 00 38 46 | 57 52 54 00 01 03 f4 00 |....d.8F|WRT.....|
|00000870| 00 00 01 00 00 00 00 00 | 00 00 00 ff ff ff ff ff |........|........|
|00000880| ff ff ff 00 00 00 08 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000890| 00 00 00 00 00 00 00 00 | 7c 00 aa 00 8b 00 b5 a1 |........||.......|
|000008a0| 00 64 00 38 46 57 52 54 | 00 01 03 f4 00 11 00 00 |.d.8FWRT|........|
|000008b0| 00 00 00 00 00 00 00 00 | ff ff ff ff ff ff ff ff |........|........|
|000008c0| 00 00 00 08 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|000008d0| 00 00 00 00 00 93 01 5c | 00 a2 01 67 31 00 93 01 |.......\|...g1...|
|000008e0| 5c 00 a2 01 67 a1 00 64 | 00 78 46 57 52 54 00 01 |\...g..d|.xFWRT..|
|000008f0| 01 00 00 11 00 01 00 00 | 00 00 00 00 00 00 ff ff |........|........|
|00000900| ff ff ff ff ff ff 00 02 | 00 01 00 00 00 00 00 00 |........|........|
|00000910| 00 00 00 00 00 00 00 00 | 00 00 00 93 01 5d 00 a0 |........|.....]..|
|00000920| 01 84 00 93 01 5d 00 93 | 01 83 00 00 00 01 00 00 |.....]..|........|
|00000930| 00 0c 00 14 01 00 00 00 | 40 00 00 00 00 00 01 00 |........|@.......|
|00000940| 00 00 00 01 00 00 00 0c | 00 14 01 00 00 00 00 00 |........|........|
|00000950| 00 00 ff ff ff ff ff ff | ff ff ff ff 00 04 00 00 |........|........|
|00000960| 44 a4 90 00 06 00 00 00 | 00 00 0d 00 27 00 00 00 |D.......|....'...|
|00000970| 00 00 0d 00 27 00 93 01 | 5d 00 a0 01 84 00 01 00 |....'...|].......|
|00000980| 00 00 00 00 00 3e 00 00 | 00 00 00 11 00 00 00 00 |.....>..|........|
|00000990| 00 10 80 00 00 00 00 10 | 80 00 00 00 00 10 80 00 |........|........|
|000009a0| 00 00 00 10 80 00 00 00 | 00 11 00 00 00 00 00 3e |........|.......>|
|000009b0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|000009c0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 a1 00 64 |........|.......d|
|000009d0| 00 38 46 57 52 54 00 01 | 03 00 00 00 00 01 00 00 |.8FWRT..|........|
|000009e0| 00 00 00 00 00 00 ff ff | ff ff ff ff ff ff 00 00 |........|........|
|000009f0| 00 08 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000a00| 00 00 00 93 01 5c 00 a2 | 01 67 a1 00 64 00 38 46 |.....\..|.g..d.8F|
|00000a10| 57 52 54 00 01 03 00 00 | 11 00 00 00 00 00 00 00 |WRT.....|........|
|00000a20| 00 00 00 ff ff ff ff ff | ff ff ff 00 00 00 08 00 |........|........|
|00000a30| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000a40| 92 00 bb 00 a1 00 c5 31 | 00 92 00 bb 00 a1 00 c5 |.......1|........|
|00000a50| a1 00 64 00 78 46 57 52 | 54 00 01 01 c4 00 11 00 |..d.xFWR|T.......|
|00000a60| 01 00 00 00 00 00 00 00 | 00 ff ff ff ff ff ff ff |........|........|
|00000a70| ff 00 02 00 01 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000a80| 00 00 00 00 00 00 92 00 | ba 00 9f 00 e1 00 92 00 |........|........|
|00000a90| ba 00 92 00 e0 00 00 00 | 01 00 00 00 0c 00 14 01 |........|........|
|00000aa0| 00 00 00 40 00 00 00 00 | 00 01 00 00 00 00 01 00 |...@....|........|
|00000ab0| 00 00 0c 00 14 01 00 00 | 00 00 00 00 00 ff ff ff |........|........|
|00000ac0| ff ff ff ff ff ff ff 00 | 04 00 00 4c a4 90 00 06 |........|...L....|
|00000ad0| 00 00 00 00 00 0d 00 27 | 00 00 00 00 00 0d 00 27 |.......'|.......'|
|00000ae0| 00 92 00 ba 00 9f 00 e1 | 00 01 00 00 00 00 00 00 |........|........|
|00000af0| 38 00 00 00 00 00 10 00 | 00 00 00 00 10 00 00 00 |8.......|........|
|00000b00| 00 00 10 00 00 00 00 00 | 10 00 00 00 00 00 10 00 |........|........|
|00000b10| 00 00 00 00 11 00 00 00 | 00 00 3f 00 00 00 00 00 |........|..?.....|
|00000b20| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000b30| 00 00 00 00 00 00 00 00 | a1 00 64 00 38 46 57 52 |........|..d.8FWR|
|00000b40| 54 00 01 03 c4 00 11 00 | 00 00 00 00 00 00 00 00 |T.......|........|
|00000b50| 00 ff ff ff ff ff ff ff | ff 00 00 00 08 00 00 00 |........|........|
|00000b60| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 7f 00 |........|........|
|00000b70| 87 00 8e 00 93 31 00 7f | 00 87 00 8e 00 93 a1 00 |.....1..|........|
|00000b80| 64 00 78 46 57 52 54 00 | 01 01 00 00 11 00 01 00 |d.xFWRT.|........|
|00000b90| 00 00 00 00 00 00 00 ff | ff ff ff ff ff ff ff 00 |........|........|
|00000ba0| 02 00 01 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000bb0| 00 00 00 00 84 00 87 00 | 91 00 ae 00 84 00 87 00 |........|........|
|00000bc0| 84 00 ad 00 00 00 01 00 | 00 00 0c 00 14 01 00 00 |........|........|
|00000bd0| 00 40 00 00 00 00 00 01 | 00 00 00 00 01 00 00 00 |.@......|........|
|00000be0| 0c 00 14 01 00 00 00 00 | 00 00 00 ff ff ff ff ff |........|........|
|00000bf0| ff ff ff ff ff 00 04 00 | 00 4b a4 90 00 06 00 00 |........|.K......|
|00000c00| 00 00 00 0d 00 27 00 00 | 00 00 00 0d 00 27 00 84 |.....'..|.....'..|
|00000c10| 00 87 00 91 00 ae 00 01 | 00 00 00 00 00 00 3b 80 |........|......;.|
|00000c20| 00 00 00 00 12 00 00 00 | 00 00 14 00 00 00 00 00 |........|........|
|00000c30| 18 00 00 00 00 00 14 00 | 00 00 00 00 12 00 00 00 |........|........|
|00000c40| 00 00 11 00 00 00 00 00 | 39 c0 00 00 00 00 00 00 |........|9.......|
|00000c50| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000c60| 00 00 00 00 00 00 a1 00 | 64 00 38 46 57 52 54 00 |........|d.8FWRT.|
|00000c70| 01 03 00 00 00 00 01 00 | 00 00 00 00 00 00 00 ff |........|........|
|00000c80| ff ff ff ff ff ff ff 00 | 00 00 08 00 00 00 00 00 |........|........|
|00000c90| 00 00 00 00 00 00 00 00 | 00 00 00 00 7f 00 87 00 |........|........|
|00000ca0| 8e 00 93 a1 00 64 00 38 | 46 57 52 54 00 01 03 00 |.....d.8|FWRT....|
|00000cb0| 00 11 00 00 00 00 00 00 | 00 00 00 00 ff ff ff ff |........|........|
|00000cc0| ff ff ff ff 00 00 00 08 | 00 00 00 00 00 00 00 00 |........|........|
|00000cd0| 00 00 00 00 00 00 00 00 | 00 97 00 8d 00 a6 00 99 |........|........|
|00000ce0| 31 00 97 00 8d 00 a6 00 | 99 a1 00 64 00 78 46 57 |1.......|...d.xFW|
|00000cf0| 52 54 00 01 01 c4 00 11 | 00 01 00 00 00 00 00 00 |RT......|........|
|00000d00| 00 00 ff ff ff ff ff ff | ff ff 00 02 00 01 00 00 |........|........|
|00000d10| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 96 |........|........|
|00000d20| 00 88 00 a3 00 af 00 96 | 00 88 00 96 00 ae 00 00 |........|........|
|00000d30| 00 01 00 00 00 0c 00 14 | 01 00 00 00 40 00 00 00 |........|....@...|
|00000d40| 00 00 01 00 00 00 00 01 | 00 00 00 0c 00 14 01 00 |........|........|
|00000d50| 00 00 00 00 00 00 ff ff | ff ff ff ff ff ff ff ff |........|........|
|00000d60| 00 04 00 00 48 a4 90 00 | 06 00 00 00 00 00 0d 00 |....H...|........|
|00000d70| 27 00 00 00 00 00 0d 00 | 27 00 96 00 88 00 a3 00 |'.......|'.......|
|00000d80| af 00 01 00 00 00 00 00 | 00 39 c0 00 00 00 00 10 |........|.9......|
|00000d90| 80 00 00 00 00 10 80 00 | 00 00 00 1f 80 00 00 00 |........|........|
|00000da0| 00 10 80 00 00 00 00 10 | 80 00 00 00 00 10 80 00 |........|........|
|00000db0| 00 00 00 39 c0 00 00 00 | 00 00 00 00 00 00 00 00 |...9....|........|
|00000dc0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000dd0| 00 a1 00 64 00 38 46 57 | 52 54 00 01 03 c4 00 00 |...d.8FW|RT......|
|00000de0| 00 01 00 00 00 00 00 00 | 00 00 ff ff ff ff ff ff |........|........|
|00000df0| ff ff 00 00 00 08 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000e00| 00 00 00 00 00 00 00 97 | 00 8d 00 a6 00 99 a1 00 |........|........|
|00000e10| 64 00 38 46 57 52 54 00 | 01 03 c4 00 11 00 00 00 |d.8FWRT.|........|
|00000e20| 00 00 00 00 00 00 00 ff | ff ff ff ff ff ff ff 00 |........|........|
|00000e30| 00 00 08 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000e40| 00 00 00 01 00 00 bb 01 | 0f 00 c2 31 01 00 00 bb |........|...1....|
|00000e50| 01 0f 00 c2 a1 00 64 00 | 78 46 57 52 54 00 01 01 |......d.|xFWRT...|
|00000e60| 00 00 11 00 01 00 00 00 | 00 00 00 00 00 ff ff ff |........|........|
|00000e70| ff ff ff ff ff 00 02 00 | 01 00 00 00 00 00 00 00 |........|........|
|00000e80| 00 00 00 00 00 00 00 00 | 00 01 04 00 b7 01 11 00 |........|........|
|00000e90| de 01 04 00 b7 01 04 00 | dd 00 00 00 01 00 00 00 |........|........|
|00000ea0| 0c 00 14 01 00 00 00 40 | 00 00 00 00 00 01 00 00 |.......@|........|
|00000eb0| 00 00 01 00 00 00 0c 00 | 14 01 00 00 00 00 00 00 |........|........|
|00000ec0| 00 ff ff ff ff ff ff ff | ff ff ff 00 04 00 00 49 |........|.......I|
|00000ed0| a4 90 00 06 00 00 00 00 | 00 0d 00 27 00 00 00 00 |........|...'....|
|00000ee0| 00 0d 00 27 01 04 00 b7 | 01 11 00 de 00 01 00 00 |...'....|........|
|00000ef0| 00 00 00 00 38 00 00 00 | 00 00 10 00 00 00 00 00 |....8...|........|
|00000f00| 10 00 00 00 00 00 10 00 | 00 00 00 00 10 00 00 00 |........|........|
|00000f10| 00 00 10 00 00 00 00 00 | 10 00 00 00 00 00 38 00 |........|......8.|
|00000f20| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000f30| 00 00 00 00 00 00 00 00 | 00 00 00 00 a1 00 64 00 |........|......d.|
|00000f40| 38 46 57 52 54 00 01 03 | 00 00 11 00 00 00 00 00 |8FWRT...|........|
|00000f50| 00 00 00 00 00 ff ff ff | ff ff ff ff ff 00 00 00 |........|........|
|00000f60| 08 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000f70| 00 00 92 00 78 00 a1 00 | 82 31 00 92 00 78 00 a1 |....x...|.1...x..|
|00000f80| 00 82 a1 00 64 00 79 46 | 57 52 54 00 01 01 c4 00 |....d.yF|WRT.....|
|00000f90| 11 00 01 00 00 00 00 00 | 00 00 00 ff ff ff ff ff |........|........|
|00000fa0| ff ff ff 00 02 00 01 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000fb0| 00 00 00 00 00 00 00 00 | 8f 00 78 00 9c 00 9f 00 |........|..x.....|
|00000fc0| 8f 00 78 00 8f 00 9e 00 | 00 00 01 00 00 00 0c 00 |..x.....|........|
|00000fd0| 14 01 00 00 00 40 00 00 | 00 00 00 01 00 00 00 00 |.....@..|........|
|00000fe0| 01 00 00 00 0c 00 14 01 | 00 00 00 00 00 00 00 ff |........|........|
|00000ff0| ff ff ff ff ff ff ff ff | ff 00 04 00 00 81 4f a4 |........|......O.|
|00001000| 90 00 06 00 00 00 00 00 | 0d 00 27 00 00 00 00 00 |........|..'.....|
|00001010| 0d 00 27 00 8f 00 78 00 | 9c 00 9f 00 01 00 00 00 |..'...x.|........|
|00001020| 00 00 00 0e 00 00 00 00 | 00 11 00 00 00 00 00 20 |........|....... |
|00001030| 80 00 00 00 00 20 80 00 | 00 00 00 20 80 00 00 00 |..... ..|... ....|
|00001040| 00 20 80 00 00 00 00 11 | 00 00 00 00 00 0e 00 00 |. ......|........|
|00001050| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00001060| 00 00 00 00 00 00 00 00 | 00 00 00 a1 00 64 00 38 |........|.....d.8|
|00001070| 46 57 52 54 00 01 03 c4 | 00 00 00 01 00 00 00 00 |FWRT....|........|
|00001080| 00 00 00 00 ff ff ff ff | ff ff ff ff 00 00 00 08 |........|........|
|00001090| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|000010a0| 00 92 00 78 00 a1 00 82 | a1 00 64 00 7c 46 57 52 |...x....|..d.|FWR|
|000010b0| 54 00 01 01 00 00 11 00 | 01 00 00 00 00 00 00 00 |T.......|........|
|000010c0| 00 ff ff ff ff ff ff ff | ff 00 02 00 01 00 00 00 |........|........|
|000010d0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 84 01 |........|........|
|000010e0| 09 00 91 01 30 00 84 01 | 09 00 84 01 2f 00 00 00 |....0...|..../...|
|000010f0| 01 00 00 00 0c 00 03 01 | 00 00 00 40 00 00 00 00 |........|...@....|
|00001100| 00 01 00 00 00 00 01 00 | 00 00 0c 00 03 01 00 00 |........|........|
|00001110| 00 00 00 00 00 ff ff ff | ff ff ff ff ff ff ff 00 |........|........|
|00001120| 04 00 00 c1 00 14 81 65 | a4 90 00 06 00 00 00 00 |.......e|........|
|00001130| 00 0d 00 27 00 00 00 00 | 00 0d 00 27 00 84 01 09 |...'....|...'....|
|00001140| 00 91 01 30 00 01 00 00 | 00 00 00 00 00 00 00 00 |...0....|........|
|00001150| 00 00 00 00 00 00 00 00 | 18 00 00 00 00 00 24 00 |........|......$.|
|00001160| 00 00 00 00 3c 00 00 00 | 00 00 20 00 00 00 00 00 |....<...|.. .....|
|00001170| 24 00 00 00 00 00 18 00 | 00 00 00 00 00 00 00 00 |$.......|........|
|00001180| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00001190| 00 00 00 00 ff 00 00 00 | 01 00 00 00 dc 00 00 00 |........|........|
|000011a0| 2a 00 8f fe a0 00 8f fe | 9c 00 00 31 2e 20 20 57 |*.......|...1. W|
|000011b0| 68 65 6e 20 74 68 65 20 | 70 6f 69 6e 74 73 20 41 |hen the |points A|
|000011c0| 2c 20 42 2c 20 43 20 61 | 6e 64 20 44 20 61 72 65 |, B, C a|nd D are|
|000011d0| 20 63 6f 6c 6c 69 6e 65 | 61 72 20 74 68 65 6e 20 | colline|ar then |
|000011e0| 74 68 65 20 69 73 6f 70 | 74 69 63 20 63 75 62 69 |the isop|tic cubi|
|000011f0| 63 20 69 73 20 72 65 64 | 75 63 69 62 6c 65 20 69 |c is red|ucible i|
|00001200| 6e 74 6f 20 74 68 65 20 | 73 75 70 70 6f 72 74 69 |nto the |supporti|
|00001210| 6e 67 20 6c 69 6e 65 20 | 65 20 6f 66 20 74 68 65 |ng line |e of the|
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|00001230| 72 63 6c 65 20 77 69 74 | 68 20 64 69 61 6d 65 74 |rcle wit|h diamet|
|00001240| 65 72 73 20 74 68 65 20 | 74 77 6f 20 70 6f 69 6e |ers the |two poin|
|00001250| 74 73 20 4f 2c 20 4f 27 | 20 6f 66 20 65 2c 20 77 |ts O, O'| of e, w|
|00001260| 68 69 63 68 20 68 61 76 | 65 20 74 68 65 20 70 72 |hich hav|e the pr|
|00001270| 6f 70 65 72 74 79 20 20 | 4f 42 2f 4f 43 20 3d 20 |operty |OB/OC = |
|00001280| 4f 41 2f 4f 44 20 2e 00 | 02 00 00 00 00 00 10 00 |OA/OD ..|........|
|00001290| 0c 00 00 00 00 00 0c dd | dd 00 00 00 00 00 00 00 |........|........|
|000012a0| 02 00 10 00 0c 00 00 00 | 00 00 0c 00 00 00 00 00 |........|........|
|000012b0| 00 00 00 00 03 00 00 02 | 03 00 00 00 66 00 8f fe |........|....f...|
|000012c0| 94 00 8f fe 90 00 00 09 | 49 6e 20 66 61 63 74 2c |........|In fact,|
|000012d0| 20 6c 65 74 20 50 49 20 | 62 65 20 74 68 65 20 63 | let PI |be the c|
|000012e0| 6f 6d 6d 6f 6e 20 62 69 | 73 73 65 63 74 72 69 63 |ommon bi|ssectric|
|000012f0| 65 20 6f 66 20 74 68 65 | 20 61 6e 67 6c 65 73 20 |e of the| angles |
|00001300| d0 41 50 44 20 61 6e 64 | 20 20 d0 42 50 43 2e 20 |.APD and| .BPC. |
|00001310| 20 54 68 65 6e 20 77 65 | 20 68 61 76 65 20 7c 4f | Then we| have |O|
|00001320| 48 7c 7c 4f 50 7c 20 3d | 20 7c 42 4f 7c 7c 4f 43 |H||OP| =| |BO||OC|
|00001330| 7c 20 61 6e 64 20 7c 4f | 49 7c 7c 4f 50 7c 20 3d || and |O|I||OP| =|
|00001340| 20 7c 41 4f 7c 7c 4f 44 | 7c 2e 20 20 54 68 65 73 | |AO||OD||. Thes|
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|00001360| 48 2c 20 43 20 6c 69 65 | 20 6f 6e 20 6f 6e 65 20 |H, C lie| on one |
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|00001380| 20 49 2c 20 44 20 6c 69 | 65 20 61 6c 73 6f 20 6f | I, D li|e also o|
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|000013a0| 09 49 74 20 66 6f 6c 6c | 6f 77 73 20 74 68 61 74 |.It foll|ows that|
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|000013c0| 4f 7c 7c 4f 43 7c 2f 28 | 7c 41 4f 7c 7c 4f 44 7c |O||OC|/(||AO||OD||
|000013d0| 29 2e 20 20 54 61 6b 69 | 6e 67 20 7c 4f 4b 7c 20 |). Taki|ng |OK| |
|000013e0| 3d 20 78 20 61 6e 64 20 | 6b 6e 6f 77 69 6e 67 20 |= x and |knowing |
|000013f0| 74 68 61 74 20 74 68 65 | 20 74 72 69 61 6e 67 6c |that the| triangl|
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|00001430| 20 3a 0d 09 78 2f 28 78 | 2b 7c 4b 4c 7c 29 20 3d | :..x/(x|+|KL|) =|
|00001440| 20 28 7c 42 4b 7c 2d 78 | 29 28 7c 42 4b 7c 2b 78 | (|BK|-x|)(|BK|+x|
|00001450| 29 2f 28 7c 41 4c 7c 2d | 28 7c 4b 4c 7c 2b 78 29 |)/(|AL|-|(|KL|+x)|
|00001460| 29 28 7c 41 4c 7c 2b 28 | 7c 4b 4c 7c 2b 78 29 29 |)(|AL|+(||KL|+x))|
|00001470| 2e 0d 54 68 69 73 20 67 | 69 76 65 73 20 61 20 71 |..This g|ives a q|
|00001480| 75 61 64 72 61 74 69 63 | 20 65 71 75 61 74 69 6f |uadratic| equatio|
|00001490| 6e 20 66 6f 72 20 78 2c | 20 77 68 69 63 68 20 64 |n for x,| which d|
|000014a0| 65 74 65 72 6d 69 6e 65 | 73 20 74 68 65 20 74 77 |etermine|s the tw|
|000014b0| 6f 20 70 6f 69 6e 74 73 | 20 4f 2c 20 4f 27 20 20 |o points| O, O' |
|000014c0| 61 73 20 73 74 61 74 65 | 64 2e 00 05 00 00 00 00 |as state|d.......|
|000014d0| 00 10 00 0c 00 00 00 00 | 00 0c 00 00 00 00 00 00 |........|........|
|000014e0| 00 00 00 39 00 12 00 0d | 00 17 00 00 00 0c 00 00 |...9....|........|
|000014f0| 00 00 00 00 00 00 00 3a | 00 10 00 0c 00 00 00 00 |.......:|........|
|00001500| 00 0c 00 00 00 00 00 00 | 00 00 00 43 00 12 00 0d |........|...C....|
|00001510| 00 17 00 00 00 0c 00 00 | 00 00 00 00 00 00 00 44 |........|.......D|
|00001520| 00 10 00 0c 00 00 00 00 | 00 0c 00 00 00 00 00 00 |........|........|
|00001530| 00 00 00 03 00 00 07 9f | 00 00 02 5a 00 8f fe 88 |........|...Z....|
|00001540| 00 8f fe 84 00 d8 0d 32 | 2e 20 20 53 68 6f 77 2c |.......2|. Show,|
|00001550| 20 75 73 69 6e 67 20 74 | 68 65 20 63 61 6e 6f 6e | using t|he canon|
|00001560| 69 63 61 6c 20 66 6f 72 | 6d 20 6f 66 20 41 70 6f |ical for|m of Apo|
|00001570| 6c 6c 6f 6e 69 61 6e 20 | 63 75 62 69 63 73 2c 20 |llonian |cubics, |
|00001580| 74 68 61 74 20 74 68 65 | 72 65 20 61 72 65 20 73 |that the|re are s|
|00001590| 75 63 68 20 63 75 62 69 | 63 73 20 68 61 76 69 6e |uch cubi|cs havin|
|000015a0| 67 20 6f 6e 65 20 66 6c | 65 78 20 61 74 20 69 6e |g one fl|ex at in|
|000015b0| 66 69 6e 69 74 79 2c 20 | 61 6e 64 20 74 68 61 74 |finity, |and that|
|000015c0| 20 74 68 65 73 65 20 63 | 75 62 69 63 73 20 61 72 | these c|ubics ar|
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|000015e0| 20 72 65 73 70 65 63 74 | 20 74 6f 20 61 6e 20 61 | respect| to an a|
|000015f0| 78 65 73 2c 20 6f 72 74 | 68 6f 67 6f 6e 61 6c 20 |xes, ort|hogonal |
|00001600| 74 6f 20 74 68 65 20 61 | 73 79 6d 70 74 6f 74 65 |to the a|symptote|
|00001610| 2e 0d 0d 33 2e 20 20 46 | 69 6e 64 20 61 6c 6c 20 |...3. F|ind all |
|00001620| 73 69 6e 67 75 6c 61 72 | 20 41 70 6f 6c 6c 6f 6e |singular| Apollon|
|00001630| 69 61 6e 20 63 75 62 69 | 63 73 2c 20 77 68 69 63 |ian cubi|cs, whic|
|00001640| 68 20 68 61 76 65 20 69 | 6e 74 65 67 72 61 6c 20 |h have i|ntegral |
|00001650| 63 6f 65 66 66 69 63 69 | 65 6e 74 73 20 61 2c 20 |coeffici|ents a, |
|00001660| 62 2c 20 63 2e 0d 5b 53 | 68 6f 77 20 74 68 61 74 |b, c..[S|how that|
|00001670| 20 74 68 65 79 20 61 72 | 65 20 67 69 76 65 6e 20 | they ar|e given |
|00001680| 62 79 3a 20 20 0d 09 09 | 09 09 09 09 09 09 09 09 |by: ...|........|
|00001690| 09 09 09 09 09 09 09 09 | 09 09 09 09 09 09 61 20 |........|......a |
|000016a0| 3d 20 b1 32 6b 20 20 20 | 20 20 28 6b ad 30 29 2c |= .2k | (k.0),|
|000016b0| 7f 0d 09 09 09 09 09 09 | 09 09 09 09 09 09 09 09 |........|........|
|000016c0| 09 09 09 09 09 09 09 09 | 09 09 62 20 3d 20 6b 82 |........|..b = k.|
|000016d0| 20 2d 20 6d 82 2c 20 20 | 0d 09 09 09 09 09 09 09 | - m., |........|
|000016e0| 09 09 09 09 09 09 09 09 | 09 09 09 09 09 09 09 09 |........|........|
|000016f0| 20 20 63 20 3d 20 b1 32 | 6b 6d 2e 0d 0d 34 2e 20 | c = .2|km...4. |
|00001700| 20 20 53 68 6f 77 20 74 | 68 61 74 20 77 68 65 6e | Show t|hat when|
|00001710| 20 74 68 65 20 63 75 62 | 69 63 20 63 3d 41 50 28 | the cub|ic c=AP(|
|00001720| 41 44 2c 42 43 29 20 68 | 61 73 20 74 77 6f 20 63 |AD,BC) h|as two c|
|00001730| 6f 6d 70 6f 6e 65 6e 74 | 73 2c 20 74 68 65 6e 20 |omponent|s, then |
|00001740| 66 6f 72 20 65 76 65 72 | 79 20 70 6f 69 6e 74 20 |for ever|y point |
|00001750| 50 20 6f 6e 20 63 20 74 | 68 65 20 61 6e 67 6c 65 |P on c t|he angle|
|00001760| 73 20 76 69 65 77 69 6e | 67 20 74 68 65 20 74 77 |s viewin|g the tw|
|00001770| 6f 20 63 6f 6d 70 6f 6e | 65 6e 74 73 20 66 72 6f |o compon|ents fro|
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|00001790| 20 73 75 70 70 6c 65 6d | 65 6e 74 61 72 79 2e 0d | supplem|entary..|
|000017a0| 0d 35 2e 20 20 20 53 68 | 6f 77 20 74 68 61 74 20 |.5. Sh|ow that |
|000017b0| 74 68 65 20 77 69 64 74 | 68 20 64 20 6f 66 20 74 |the widt|h d of t|
|000017c0| 68 65 20 62 6f 75 6e 64 | 65 64 20 63 6f 6d 70 6f |he bound|ed compo|
|000017d0| 6e 65 6e 74 20 62 65 74 | 77 65 65 6e 20 70 61 72 |nent bet|ween par|
|000017e0| 61 6c 6c 65 6c 20 74 61 | 6e 67 65 6e 74 73 20 74 |allel ta|ngents t|
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|00001830| 75 6e 64 65 64 20 63 6f | 6d 70 6f 6e 65 6e 74 20 |unded co|mponent |
|00001840| 28 77 68 65 6e 20 74 68 | 65 20 69 73 6f 70 74 69 |(when th|e isopti|
|00001850| 63 20 68 61 73 20 74 77 | 6f 20 63 6f 6d 70 6f 6e |c has tw|o compon|
|00001860| 65 6e 74 73 29 20 2e 20 | 20 20 09 0d 0d 36 2e 20 |ents) . | ...6. |
|00001870| 20 20 53 68 6f 77 20 74 | 68 61 74 20 77 68 65 6e | Show t|hat when|
|00001880| 20 74 68 65 20 63 75 62 | 69 63 20 63 3d 41 50 28 | the cub|ic c=AP(|
|00001890| 41 44 2c 42 43 29 20 68 | 61 73 20 74 77 6f 20 63 |AD,BC) h|as two c|
|000018a0| 6f 6d 70 6f 6e 65 6e 74 | 73 2c 20 74 68 65 6e 20 |omponent|s, then |
|000018b0| 66 6f 72 20 65 76 65 72 | 79 20 70 6f 69 6e 74 20 |for ever|y point |
|000018c0| 50 20 6f 66 20 63 20 74 | 68 65 20 70 6f 69 6e 74 |P of c t|he point|
|000018d0| 73 20 50 20 61 6e 64 20 | 50 2a 20 6c 69 65 20 69 |s P and |P* lie i|
|000018e0| 6e 20 64 69 66 66 65 72 | 65 6e 74 20 63 6f 6d 70 |n differ|ent comp|
|000018f0| 6f 6e 65 6e 74 73 2e 20 | 20 57 65 20 63 6f 6e 63 |onents. | We conc|
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|00001910| 65 6c 6c 20 61 73 20 4f | 31 20 6c 69 65 20 6f 6e |ell as O|1 lie on|
|00001920| 20 74 68 65 20 62 6f 75 | 6e 64 65 64 20 63 6f 6d | the bou|nded com|
|00001930| 70 6f 6e 65 6e 74 2e 09 | 0d 0d 37 2e 20 20 20 4c |ponent..|..7. L|
|00001940| 65 74 20 63 20 3d 20 41 | 50 28 41 44 2c 42 43 29 |et c = A|P(AD,BC)|
|00001950| 20 68 61 76 65 20 6f 6e | 65 20 63 6f 6d 70 6f 6e | have on|e compon|
|00001960| 65 6e 74 2e 20 4c 65 74 | 20 41 20 62 65 20 61 6e |ent. Let| A be an|
|00001970| 79 20 70 6f 69 6e 74 20 | 6f 6e 20 63 20 61 6e 64 |y point |on c and|
|00001980| 20 6c 65 74 20 41 42 2c | 20 41 42 2a 20 62 65 20 | let AB,| AB* be |
|00001990| 74 68 65 20 74 61 6e 67 | 65 6e 74 73 20 66 72 6f |the tang|ents fro|
|000019a0| 6d 20 41 20 74 6f 20 63 | 2c 20 41 2a 43 2c 20 41 |m A to c|, A*C, A|
|000019b0| 2a 43 2a 20 62 65 20 74 | 68 65 20 74 61 6e 67 65 |*C* be t|he tange|
|000019c0| 6e 74 73 20 66 72 6f 6d | 20 41 2a 20 74 6f 20 63 |nts from| A* to c|
|000019d0| 2e 20 20 50 72 6f 76 65 | 20 74 68 61 74 20 41 2c |. Prove| that A,|
|000019e0| 20 43 20 61 6e 64 20 43 | 2a 20 61 72 65 20 63 6f | C and C|* are co|
|000019f0| 6c 6c 69 6e 65 61 72 20 | 61 6e 64 20 42 41 2a 42 |llinear |and BA*B|
|00001a00| 2a 20 61 72 65 20 63 6f | 6c 6c 69 6e 65 61 72 2e |* are co|llinear.|
|00001a10| 20 20 50 72 6f 76 65 20 | 74 68 61 74 20 41 43 2a | Prove |that AC*|
|00001a20| 43 20 69 73 20 74 68 65 | 20 62 69 73 73 65 63 74 |C is the| bissect|
|00001a30| 6f 72 20 28 69 6e 74 65 | 72 6e 61 6c 20 6f 72 20 |or (inte|rnal or |
|00001a40| 65 78 74 65 72 6e 61 6c | 29 20 6f 66 20 74 68 65 |external|) of the|
|00001a50| 20 61 6e 67 6c 65 20 ff | 42 41 42 2a 20 61 6e 64 | angle .|BAB* and|
|00001a60| 20 42 41 2a 42 2a 20 69 | 73 20 74 68 65 20 62 69 | BA*B* i|s the bi|
|00001a70| 73 73 65 63 74 6f 72 20 | 6f 66 20 74 68 65 20 61 |ssector |of the a|
|00001a80| 6e 67 6c 65 20 ff 43 41 | 2a 43 2a 20 28 66 69 67 |ngle .CA|*C* (fig|
|00001a90| 75 72 65 2d 32 32 29 20 | 2e 20 09 09 0d 20 20 20 |ure-22) |. ... |
|00001aa0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00001ab0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00001ac0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00001ad0| 20 20 20 20 20 5b 48 69 | 6e 74 20 3a 20 20 32 42 | [Hi|nt : 2B|
|00001ae0| 2b 41 3d 4f 20 de 20 28 | 61 64 64 69 6e 67 20 32 |+A=O . (|adding 2|
|00001af0| 4f 31 3d 4f 29 20 42 2b | 41 2a 2b 42 2a 3d 4f 2e |O1=O) B+|A*+B*=O.|
|00001b00| 5d 0d 38 2e 20 20 20 4c | 65 74 20 63 3d 41 50 28 |].8. L|et c=AP(|
|00001b10| 41 44 2c 42 43 29 2c 20 | 74 68 65 6e 20 74 68 65 |AD,BC), |then the|
|00001b20| 20 70 6f 69 6e 74 73 20 | 41 2c 20 42 2c 20 43 20 | points |A, B, C |
|00001b30| 61 6e 64 20 44 20 6c 69 | 65 20 6f 6e 20 74 68 65 |and D li|e on the|
|00001b40| 20 73 61 6d 65 20 63 69 | 72 63 6c 65 20 69 66 20 | same ci|rcle if |
|00001b50| 61 6e 64 20 6f 6e 6c 79 | 20 69 66 20 74 68 65 20 |and only| if the |
|00001b60| 74 61 6e 67 65 6e 74 20 | 61 74 20 74 68 65 20 70 |tangent |at the p|
|00001b70| 6f 69 6e 74 20 6f 66 20 | 69 6e 74 65 72 73 65 63 |oint of |intersec|
|00001b80| 74 69 6f 6e 20 6f 66 20 | 41 42 20 77 69 74 68 20 |tion of |AB with |
|00001b90| 43 44 20 69 73 20 70 61 | 72 61 6c 6c 65 6c 20 74 |CD is pa|rallel t|
|00001ba0| 6f 20 74 68 65 20 61 73 | 79 6d 70 74 6f 74 69 63 |o the as|ymptotic|
|00001bb0| 2e 20 09 0d 20 20 20 20 | 20 20 20 20 20 20 20 20 |. .. | |
|00001bc0| 5b 48 69 6e 74 20 3a 20 | 41 2c 20 42 2c 20 43 2c |[Hint : |A, B, C,|
|00001bd0| 20 44 20 6f 6e 20 61 20 | 63 69 72 63 6c 65 20 db | D on a |circle .|
|00001be0| 20 20 41 2b 42 2b 43 2b | 44 2b 49 2b 49 27 3d 4f | A+B+C+|D+I+I'=O|
|00001bf0| 20 20 db 20 2d 45 2d 45 | 2d 48 2a 3d 4f 20 28 66 | . -E-E|-H*=O (f|
|00001c00| 69 67 75 72 65 2d 32 34 | 29 20 5d 0d 0d 39 2e 20 |igure-24|) ]..9. |
|00001c10| 20 4c 65 74 20 63 20 3d | 20 41 50 28 53 53 2c 42 | Let c =| AP(SS,B|
|00001c20| 43 29 20 28 66 69 67 75 | 72 65 2d 32 39 29 20 2e |C) (figu|re-29) .|
|00001c30| 20 20 53 68 6f 77 20 74 | 68 61 74 20 42 43 20 69 | Show t|hat BC i|
|00001c40| 6e 74 65 72 73 65 63 74 | 73 20 63 20 61 74 20 59 |ntersect|s c at Y|
|00001c50| 2c 20 73 6f 20 74 68 61 | 74 20 53 59 20 69 73 20 |, so tha|t SY is |
|00001c60| 74 68 65 20 61 6c 74 69 | 74 75 64 65 20 6f 66 20 |the alti|tude of |
|00001c70| 74 68 65 20 74 72 69 61 | 6e 67 6c 65 20 42 43 53 |the tria|ngle BCS|
|00001c80| 20 66 72 6f 6d 20 53 2e | 20 20 53 68 6f 77 20 61 | from S.| Show a|
|00001c90| 6c 73 6f 20 74 68 61 74 | 20 74 68 65 20 6d 65 64 |lso that| the med|
|00001ca0| 69 61 6e 20 53 4d 20 6f | 66 20 74 68 69 73 20 74 |ian SM o|f this t|
|00001cb0| 72 69 61 6e 67 6c 65 20 | 69 73 20 70 61 72 61 6c |riangle |is paral|
|00001cc0| 6c 65 6c 20 74 6f 20 74 | 68 65 20 61 73 79 6d 70 |lel to t|he asymp|
|00001cd0| 74 6f 74 69 63 20 64 69 | 72 65 63 74 69 6f 6e 20 |totic di|rection |
|00001ce0| 6f 66 20 63 2e 00 1e 00 | 00 00 00 00 10 00 0c 00 |of c....|........|
|00001cf0| 00 00 00 00 0c dd dd 00 | 00 00 00 00 00 00 03 00 |........|........|
|00001d00| 10 00 0c 00 00 00 00 00 | 0c 00 00 00 00 00 00 00 |........|........|
|00001d10| 00 00 cd 00 10 00 0c 00 | 00 00 00 00 0c dd dd 00 |........|........|
|00001d20| 00 00 00 00 00 00 cf 00 | 10 00 0c 00 00 00 00 00 |........|........|
|00001d30| 0c 00 00 00 00 00 00 00 | 00 01 b7 00 10 00 0c 00 |........|........|
|00001d40| 00 00 00 00 0c dd dd 00 | 00 00 00 00 00 01 b9 00 |........|........|
|00001d50| 10 00 0c 00 00 00 00 00 | 0c 00 00 00 00 00 00 00 |........|........|
|00001d60| 00 02 5b 00 10 00 0c 00 | 00 00 00 00 0c dd dd 00 |..[.....|........|
|00001d70| 00 00 00 00 00 02 5d 00 | 10 00 0c 00 00 00 00 00 |......].|........|
|00001d80| 0c 00 00 00 00 00 00 00 | 00 03 27 00 10 00 0c 00 |........|..'.....|
|00001d90| 00 00 00 00 0c dd dd 00 | 00 00 00 00 00 03 29 00 |........|......).|
|00001da0| 10 00 0c 00 00 00 00 00 | 0c 00 00 00 00 00 00 00 |........|........|
|00001db0| 00 03 d2 00 15 00 0e 00 | 1a 00 00 00 0c 00 00 00 |........|........|
|00001dc0| 00 00 00 00 00 03 d3 00 | 10 00 0c 00 00 00 00 00 |........|........|
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|00003c60| 90 b0 00 81 c6 81 c6 9f | c6 aa 00 00 90 f9 00 00 |........|........|
|00003c70| 14 00 90 b0 00 fe c6 81 | 00 81 00 a5 00 fe c6 aa |........|........|
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|00003cd0| 00 81 00 a5 00 fe c6 aa | 00 00 90 f9 00 00 14 00 |........|........|
|00003ce0| 90 b0 00 fe c6 81 00 81 | 00 a5 00 fe c6 aa 00 00 |........|........|
|00003cf0| 90 f9 00 00 14 00 90 b0 | 00 fe c6 81 00 81 00 a5 |........|........|
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|00003d10| c6 81 00 81 00 a5 00 fe | c6 aa 00 00 90 f9 00 00 |........|........|
|00003d20| 14 00 90 b0 00 fe c6 81 | 00 81 00 a5 00 fe c6 aa |........|........|
|00003d30| 00 00 90 f9 00 00 14 00 | 90 b0 00 fe c6 81 00 81 |........|........|
|00003d40| 00 a5 00 fe c6 aa 00 00 | 90 f9 00 00 14 00 90 b0 |........|........|
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|00003d70| c6 aa 00 00 90 f9 00 00 | 14 00 90 b0 00 fe c6 81 |........|........|
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|00003d90| 90 b0 00 fe c6 81 00 81 | 00 a5 00 fe c6 aa 00 00 |........|........|
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|00003dc0| c6 81 00 81 00 a5 00 fe | c6 aa 00 00 90 f9 00 00 |........|........|
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|000045a0| 00 00 00 00 00 00 00 00 | ee ee 00 00 00 00 00 00 |........|........|
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|000045e0| 44 44 00 00 00 00 00 00 | 22 22 00 00 00 00 00 00 |DD......|""......|
|000045f0| 11 11 00 00 ee ee ee ee | ee ee 00 00 dd dd dd dd |........|........|
|00004600| dd dd 00 00 bb bb bb bb | bb bb 00 00 aa aa aa aa |........|........|
|00004610| aa aa 00 00 88 88 88 88 | 88 88 00 00 77 77 77 77 |........|....wwww|
|00004620| 77 77 00 00 55 55 55 55 | 55 55 00 00 44 44 44 44 |ww..UUUU|UU..DDDD|
|00004630| 44 44 00 00 22 22 22 22 | 22 22 00 00 11 11 11 11 |DD..""""|""......|
|00004640| 11 11 00 00 00 00 00 00 | 00 00 00 4e 00 00 00 9c |........|...N....|
|00004650| 02 0d 00 4e 00 00 00 9c | 02 0d 00 00 00 14 00 90 |...N....|........|
|00004660| b0 00 fe c6 81 00 81 00 | a5 00 fe c6 aa 00 00 90 |........|........|
|00004670| f9 00 00 14 00 90 b0 00 | fe c6 81 00 81 00 a5 00 |........|........|
|00004680| fe c6 aa 00 00 90 f9 00 | 00 14 00 90 b0 00 fe c6 |........|........|
|00004690| 81 00 81 00 a5 00 fe c6 | aa 00 00 90 f9 00 00 14 |........|........|
|000046a0| 00 90 b0 00 fe c6 81 00 | 81 00 a5 00 fe c6 aa 00 |........|........|
|000046b0| 00 90 f9 00 00 14 00 90 | b0 00 fe c6 81 00 81 00 |........|........|
|000046c0| a5 00 fe c6 aa 00 00 90 | f9 00 00 14 00 90 b0 00 |........|........|
|000046d0| fe c6 81 00 81 00 a5 00 | fe c6 aa 00 00 90 f9 00 |........|........|
|000046e0| 00 14 00 90 b0 00 fe c6 | 81 00 81 00 a5 00 fe c6 |........|........|
|000046f0| aa 00 00 90 f9 00 00 14 | 00 90 b0 00 fe c6 81 00 |........|........|
|00004700| 81 00 a5 00 fe c6 aa 00 | 00 90 f9 00 00 14 00 90 |........|........|
|00004710| b0 00 fe c6 81 00 81 00 | a5 00 fe c6 aa 00 00 90 |........|........|
|00004720| f9 00 00 14 00 90 b0 00 | fe c6 81 00 81 00 a5 00 |........|........|
|00004730| fe c6 aa 00 00 90 f9 00 | 00 14 00 90 b0 00 fe c6 |........|........|
|00004740| 81 00 81 00 a5 00 fe c6 | aa 00 00 90 f9 00 00 14 |........|........|
|00004750| 00 90 b0 00 fe c6 81 00 | 81 00 a5 00 fe c6 aa 00 |........|........|
|00004760| 00 90 f9 00 00 14 00 90 | b0 00 fe c6 81 00 81 00 |........|........|
|00004770| a5 00 fe c6 aa 00 00 90 | f9 00 00 14 00 90 b0 00 |........|........|
|00004780| fe c6 81 00 81 00 a5 00 | fe c6 aa 00 00 90 f9 00 |........|........|
|00004790| 00 14 00 90 b0 00 fe c6 | 81 00 81 00 a5 00 fe c6 |........|........|
|000047a0| aa 00 00 90 f9 00 00 14 | 00 90 b0 00 fe c6 81 00 |........|........|
|000047b0| 81 00 a5 00 fe c6 aa 00 | 00 90 f9 00 00 14 00 90 |........|........|
|000047c0| b0 00 fe c6 81 00 81 00 | a5 00 fe c6 aa 00 00 90 |........|........|
|000047d0| f9 00 00 14 00 90 b0 00 | fe c6 81 00 81 00 a5 00 |........|........|
|000047e0| fe c6 aa 00 00 90 f9 00 | 00 14 00 90 b0 00 fe c6 |........|........|
|000047f0| 81 00 81 00 a5 00 fe c6 | aa 00 00 90 f9 00 00 14 |........|........|
|00004800| 00 90 b0 00 fe c6 81 00 | 81 00 a5 00 fe c6 aa 00 |........|........|
|00004810| 00 90 f9 00 00 14 00 90 | b0 00 fe c6 81 00 81 00 |........|........|
|00004820| a5 00 fe c6 aa 00 00 90 | f9 00 00 14 00 90 b0 00 |........|........|
|00004830| fe c6 81 00 81 00 a5 00 | fe c6 aa 00 00 90 f9 00 |........|........|
|00004840| 00 14 00 90 b0 00 fe c6 | 81 00 81 00 a5 00 fe c6 |........|........|
|00004850| aa 00 00 90 f9 00 00 14 | 00 90 b0 00 fe c6 81 00 |........|........|
|00004860| 81 00 a5 00 fe c6 aa 00 | 00 90 f9 00 00 14 00 90 |........|........|
|00004870| b0 00 fe c6 81 00 81 00 | a5 00 fe c6 aa 00 00 90 |........|........|
|00004880| f9 00 00 14 00 90 b0 00 | fe c6 81 00 81 00 a5 00 |........|........|
|00004890| fe c6 aa 00 00 90 f9 00 | 00 14 00 90 b0 00 fe c6 |........|........|
|000048a0| 81 00 81 00 a5 00 fe c6 | aa 00 00 90 f9 00 00 14 |........|........|
|000048b0| 00 90 b0 00 fe c6 81 00 | 81 00 a5 00 fe c6 aa 00 |........|........|
|000048c0| 00 90 f9 00 00 14 00 90 | b0 00 fe c6 81 00 81 00 |........|........|
|000048d0| a5 00 fe c6 aa 00 00 90 | f9 00 00 14 00 90 b0 00 |........|........|
|000048e0| fe c6 81 00 81 00 a5 00 | fe c6 aa 00 00 90 f9 00 |........|........|
|000048f0| 00 14 00 90 b0 00 fe c6 | 81 00 81 00 a5 00 fe c6 |........|........|
|00004900| aa 00 00 90 f9 00 00 14 | 00 90 b0 00 fe c6 81 00 |........|........|
|00004910| 81 00 a5 00 fe c6 aa 00 | 00 90 f9 00 00 14 00 90 |........|........|
|00004920| b0 00 fe c6 81 00 81 00 | a5 00 fe c6 aa 00 00 90 |........|........|
|00004930| f9 00 00 14 00 90 b0 00 | fe c6 81 00 81 00 a5 00 |........|........|
|00004940| fe c6 aa 00 00 90 f9 00 | 00 14 00 90 b0 00 fe c6 |........|........|
|00004950| 81 00 81 00 a5 00 fe c6 | aa 00 00 90 f9 00 00 14 |........|........|
|00004960| 00 90 b0 00 fe c6 81 00 | 81 00 a5 00 fe c6 aa 00 |........|........|
|00004970| 00 90 f9 00 00 14 00 90 | b0 00 fe c6 81 00 81 00 |........|........|
|00004980| a5 00 fe c6 aa 00 00 90 | f9 00 00 14 00 90 b0 00 |........|........|
|00004990| fe c6 81 00 81 00 a5 00 | fe c6 aa 00 00 90 f9 00 |........|........|
|000049a0| 00 14 00 90 b0 00 fe c6 | 81 00 81 00 a5 00 fe c6 |........|........|
|000049b0| aa 00 00 90 f9 00 00 14 | 00 90 b0 00 fe c6 81 00 |........|........|
|000049c0| 81 00 a5 00 fe c6 aa 00 | 00 90 f9 00 00 14 00 90 |........|........|
|000049d0| b0 00 fe c6 81 00 81 00 | a5 00 fe c6 aa 00 00 90 |........|........|
|000049e0| f9 00 00 14 00 90 b0 00 | fe c6 81 00 81 00 a5 00 |........|........|
|000049f0| fe c6 aa 00 00 90 f9 00 | 00 14 00 90 b0 00 fe c6 |........|........|
|00004a00| 81 00 81 00 a5 00 fe c6 | aa 00 00 90 f9 00 00 14 |........|........|
|00004a10| 00 90 b0 00 fe c6 81 00 | 81 00 a5 00 fe c6 aa 00 |........|........|
|00004a20| 00 90 f9 00 00 14 00 90 | b0 00 fe c6 81 00 81 00 |........|........|
|00004a30| a5 00 fe c6 aa 00 00 90 | f9 00 00 16 00 90 b0 00 |........|........|
|00004a40| fe c6 94 00 00 ee 81 00 | 93 00 fe c6 aa 00 00 90 |........|........|
|00004a50| f9 00 00 16 00 90 b0 00 | fe c6 a1 00 f2 ee 81 00 |........|........|
|00004a60| 94 00 fe c6 aa 00 00 90 | f9 00 00 1a 00 90 b0 00 |........|........|
|00004a70| fe c6 a4 00 fd ee fa 00 | fa ee 81 00 94 00 fe c6 |........|........|
|00004a80| aa 00 00 90 f9 00 00 1a | 00 90 b0 00 fe c6 a6 00 |........|........|
|00004a90| fd ee f6 00 fc ee 81 00 | 94 00 fe c6 aa 00 00 90 |........|........|
|00004aa0| f9 00 00 20 00 90 b0 00 | fe c6 a8 00 fd ee f3 00 |... ....|........|
|00004ab0| fd ee c5 00 00 ee c3 00 | 00 ee 90 00 fe c6 aa 00 |........|........|
|00004ac0| 00 90 f9 00 00 20 00 90 | b0 00 fe c6 a9 00 fd ee |..... ..|........|
|00004ad0| f1 00 fe ee c5 00 00 ee | c3 00 00 ee 90 00 fe c6 |........|........|
|00004ae0| aa 00 00 90 f9 00 00 23 | 00 90 b0 00 fe c6 aa 00 |.......#|........|
|00004af0| fc ee f0 00 01 ee ee c6 | 00 01 ee ee c4 00 01 ee |........|........|
|00004b00| ee 90 00 fe c6 aa 00 00 | 90 f9 00 00 21 00 90 b0 |........|....!...|
|00004b10| 00 fe c6 ab 00 fc ee ef | 00 01 ee ee c7 00 fe ee |........|........|
|00004b20| c5 00 fe ee 90 00 fe c6 | aa 00 00 90 f9 00 00 20 |........|....... |
|00004b30| 00 90 b0 00 fe c6 ac 00 | fb ee ee 00 00 ee c9 00 |........|........|
|00004b40| fc ee c7 00 fc ee 90 00 | fe c6 aa 00 00 90 f9 00 |........|........|
|00004b50| 00 3e 00 90 b0 00 fe c6 | ac 00 fc ee e1 00 fa ee |.>......|........|
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