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Theorem 1 - Equal chords of a Circle Subtend Equal Angles at the Centre

Theorem 1: Equal chords of a circle (or of congruent circles) subtend equal angles at the centre (or at the corresponding centres).
Given: PQ and RS are two equal chords of circle C(O, r)
To Prove:
POQ =ROS

Proof:
In
ΔPOQ and ΔROS,
OP = OS (radii of the same circle)
OQ = OR (radii of the same circle)
PQ = RS  (Given)

..ΔPOQ  @  DROS (SSS rule)
..POQ = ROS.





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