If the angles subtended by the chords of a circle at the center are equal , then the chords are equal.

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Solution

To Prove: $A B = C D$
Proof:- In $△ A O B & △ D O C$

$O A = O D [r a d i u s], ∠ A O B = ∠ D O C (g i v e n)$

$O B = O C (r a d i u s)$

$∴ △ A O B ≅ △ C O D$ [SAS congr]

$∴ A B = C D$ [By cpct]

Hence proved.

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