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Converse of Theorem 1

Converse : If the angles subtended by two chords of a circle (or of congruent circles) at the centre (or corresponding centres) are equal, the chords will be equal.
Given : Two chords PQ and RS of a circle C(O, r), such that POQ = ROS.
To Prove : PQ = RS.


In Δ POQ and Δ ROS 
OP = OQ = OR = OS = (radii of the same circle) and POQ = ROS
..Δ POQ Δ ROS   [SAS rule]
PQ = RS.

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