Question

If the angles subtended by the chords at the centre (of a circle) are equal then the chords are equal. Prove that.

Answer 1

Given: A circle with centre O. Chords PQ and RS subtend equal angles at the enter of the circle. 

i.e. ∠POQ = ∠ROS 

To Prove : Chord PQ = chord RS. 

Proof : In ∆POQ and ∆ROS, 

∠POQ = ∠ROS [Given] 

OP = OR [Radii of the same circle] 

OQ = OS [Radii of the same circle] 

⇒ ∆POQ ≅ ∆ROS [By SSS] 

⇒ chord PQ = chord RS [By cpctc]