Recall that two circles are congruent if they have the small radii. Then the angles subtended by the equal chord to the centres are

Unequal

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equal

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not related at all

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equal under certain conditions only.

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Solution

The correct option is B equal
$G i v e n - A & B a r e t w o c o n g r u e n t c i r c l e s w i t h e q u a l c h o r d s P Q & S T r e s p e c t i v e l y . T o p r o v e t h a t - P Q & S T s u b t e n d e q u a l a n g l e s t o t h e c e n t r e . i . e ∠ P A Q = ∠ S B T . P r o o f - W e k n o w t h a t c o n g r u e n t c i r c l e s h a v e e q u a l r a d i i . ∴ A P = A Q = B S = B T = r . S o, b e t w e e n Δ P A Q & Δ B S T w e h a v e A P = A Q = B S = B T = r a n d P Q = S T . ∴ B y S S S t e s t, Δ P A Q ≅ Δ B S T ⟹ ∠ P A Q = ∠ S B T . S o P Q & S T s u b t e n d e q u a l a n g l e s t o t h e c e n t r e . Q . E . D . A n s - O p t i o n B .$

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