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Given is AB the diameter of circle and CD is a chord equal to the radius of the circle. AC & BD when extended intersect at a point E.Then Prove that Angle AEB = 60.

Asked by singhaivk05 25th February 2015, 5:33 PM
Answered by Expert
Answer:
C o n s i d e r space t h e space f o l l o w i n g space f i g u r e.
J o i n space O C space a n d space O D. W e space h a v e comma space O A equals O B equals O C equals O D equals C D. T h u s comma space triangle C O D space i s space a n space e q u i l a t e r a l space t r i a n g l e. therefore angle C O D equals 60 degree T h e space a n g l e space s u b t e n d e d space a t space t h e space c e n t e r space o f space a space c i r c l e space b y space a space c h o r d space h a s space m e a s u r e space t w i c e space t h a t space o f space a n space a n g l e space s u b t e n d e d space o n space t h e space p e r i m e t e r space b y space t h e space s a m e space c h o r d. T h u s comma space angle C B D equals fraction numerator 60 degree over denominator 2 end fraction equals 30 degree S i n c e space A B space i s space t h e space d i a m e t e r space a n d space C space i s space a space p o i n t space o n space t h e space s e m i space c i r c l e comma space w e space h a v e comma space angle A C B equals 90 degree rightwards double arrow angle B C E equals 90 degree space space space space space open square brackets because angle A C B space a n d space angle B C E space a r e space l i n e a r space p a i r close square brackets N o w space c o n s i d e r space t h e space t r i a n g l e space triangle C B E. B y space a n g l e space s u m space p r o p e r t y comma space w e space h a v e comma angle B C E plus angle C B E plus angle C E B equals 180 degree rightwards double arrow 90 degree plus 30 degree plus angle C E B equals 180 degree rightwards double arrow angle C E B equals 180 degree minus 90 degree minus 30 degree rightwards double arrow angle C E B equals 180 degree minus 120 degree rightwards double arrow angle C E B equals 60 degree rightwards double arrow angle A E B equals 60 degree
Answered by Expert 26th February 2015, 10:57 AM
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