Question

prove that if chords of congruent circles subtend equal angles at their Centre then the chords are equal

Answer 1

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Answer 2

Statement : If the angle subtended by the chords of a circle at the centre are equal, then the chords are equal.

Given : Two chords PQ and RS of a circle
C (O , r ), such that ∠POQ = ∠ROS.

To prove : PQ = R

Proof :

In ΔPOQ and ΔROS,

OP = OQ = OR = OS = r [radii of same circle]
∠POQ = ∠ROS [Given]

ΔPOQ ≅ ΔROS [ SAS ]
PQ = RS [C. P. C. T]

Hence, If the angle subtended by the chords of a circle at the centre are equal, then the chords are equal.