:SB :SC226038200053248053248053 :SH0535C :SH0737B :SH0830O :SF D. Angles of a Circle. Make sure you know these theorems, definitions and assumptions. NOTE: < = Angle ^ = Degrees 1. A central angle is measured by its intercepted arc. Stated otherwise, a central angle is equal in degrees to its intercepted arc. <COB = degrees in BC :RA :SD :SB :SC190035155056226038226038 :SH0724A :SH0534B :SH0430C :SF 2. An inscribed angle is equal in degrees to one-half its intercepted arc. <CAB = 1/2 degrees in BC 3. In a circle, a diameter is twice the radius and divides the circle into two semicircles :RA :SD :SB :SC154056245056215035154056 :SH0824A :SH0838B :SH0434C :SF 4. An angle inscribed in a semicircle is a right angle. <ACB = 90^ :RA :SD :SB :SC202056172071226071226071 :SH0731O :SH1027A :SH1034B :SF Example: Given: Circle O; AB = 60^, OA = 6" Find: Length of AB 1. Draw radius OB. 2. Since AB = 60^, <AOB = 60^. 3. Since OA = OB, <A = <B. 4. But <A + <B = 180^ - <O = 180^ -60^ = 120^ 5. Then, <A = <B = 60^ = <O 6. Since { AOB is equiangular, it is equilateral; OA = OB = AB = 6" Ans. :RA :SD :Q :SB :SC153055247055200055214033 :SH0723A :SH0738B :SH0431C :SH0831O :SH0729y :SF 1. Given: Circle O, diameter AB, radius OC, BC = 80^. Find: Number of degrees in <y. (a) 40 (b) 80 (c) 100 (d) 140 (e) 0 :RCC 1. (c) 100 Ans. The central angle of a circle is equal to its intercepted arc. Therefore: <COB = 80^ Since y + <COB are on the same side of a straight line about a central point, they total 180^ y + 80^ = 180^ y = 100^ Ans. :RA :SD :Q :SB :SC173038231038204074204035 :SP204035173038173038173038 :SH0525A :SH1131B :SH0431C :SH0536D :SF 2. Given: Circle O, <A = 30^. Find: Number of degrees in <B. (a) 15 (b) 30 (c) 60 (d) 90 (e) 10 :RCB 2. (b) 30 Ans. Angle A and Angle B intercept the same arc CD and are therefore equal. <B = <A = 30^ Ans. :RA :SD :Q :SB :SC152056248056210056196035 :SP152056196035196035196035 :SH0724A :SH0738B :SH0430C :SH0831O :SF 3. Given: Circle O, diameter AB, radius OC, <COB = 100^. Find: Number of degrees in <A. (a) 50 (b) 90 (c) 100 (d) 200 (e) 150 :RCA 3. (a) 50 Ans. An inscribed angle is equal in degrees to one half its intercepted arc. Since <A intercepts the same arc as <COB, <A = 1/2 <COB = 1/2 (100^) = 50^ Ans. :SD :ET :ET
