If chords AB and CD of congruent circles subtend equal angles at their centres, then which of the option is correct?

A B = C D

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A B > C D

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A B < C D

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None of the above

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Solution

The correct option is A
$A B = C D$
In triangles AOB and COD,

$∠ A O B = ∠ C O D (G i v e n) O A = O C a n d O B = O D (radii of the circle) S o, Δ A O B ≅ Δ C O D . (SAS congruency) ∴ A B = C D (B y C P C T)$

Hence, the correct option is (a)

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Question 2
Prove that if chords of congruent circles subtend equal angles at their centres, then the chords are equal.

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