Two congruent circles with centres O and O' intersect at two points A and B. Then $∠ A O B = ∠ A O^{'} B$ .
State True or False.

cannot be decided

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False

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True

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All of the options.

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Solution

The correct option is C True
$G i v e n - O & O^{'} a r e t h e c e n t r e s o f t w o c o n g r u e n t c i r c l e s t h a t i n t e r s e c t a t A & B . T o f i n d o u t - I f ∠ A O B & ∠ A O^{'} B a r e e q u a l . S o l u t i o n - W e j o i n A O, A O^{'} & A B . N o w, A B i s t h e c o m m o n c h o r d o f t h e g i v e n c o n g r u e n t c i r c l e s . W e k n o w t h a t t h e c o m m o n c h o r d o f t w o c o n g r u e n t c i r c l e s s u b t e n d s e q u a l a n g l e s a t t h e c e n t e r s o f t h e c i r c l e s . ∴ ∠ A O B = ∠ A O^{'} B . S o t h e s t a t e m e n t i s c o r r e c t . A n s - O p t i o n C .$

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∠ A O B = ∠ A O^{'} B

∠ A O B = ∠ A O^{'} B

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