NetNews Usenet Archive 1993 #3/NN_1993_3.iso/spool/rec/puzzles/8599

Internet Message Format | 1993-01-28 | 1.6 KB

Path: sparky!uunet!indetech!pacbell!osc!vivekr
From: [e-mail] (Vivek Rau)
Newsgroups: rec.puzzles
Subject: Re: Geometry Puzzler
Message-ID: <[e-mail]>
Date: 26 Jan 93 22:15:27 GMT
References: <[e-mail]> <[e-mail]> <[e-mail]>
Reply-To: [e-mail] (Vivek Rau)
Organization: Versant Object Technology, Menlo Park, CA
Lines: 26

Got my A's and B's mixed up there. Here's the correction in the construction
of the inverse of a point C with respect to a circle of radius AB:

    .________.________.
    A        B        C

>    Draw a circle centred at A, radius AB. Use C as centre and mark points
>    P and P' on the circumference of this circle, by drawing an arc with
>    radius CA. Now draw arcs centred at P and P' respectively, with radius
>    PB. These arcs will intersect at 2 points, one is B itself, the
>    other is the point D which is the bisection point you are looking for.
>    For proof, consider the similar triangles APC and CPD, and remember the
>    definition of the inverse point.

Draw a circle centred at A, radius AB. Use C as centre and mark points
P and P' on the circumference of this circle, by drawing an arc with
radius CA. Now draw arcs centred at P and P' respectively, with radius
PA. These arcs will intersect at 2 points, one is A itself, the
^^                                                ^
other is the point D which is the bisection point you are looking for.
For proof, consider the similar triangles APC and APD, and remember the
                                                  ^
definition of the inverse point.

Vivek Rau
[e-mail]