Question

PQ and RS are two parallel chords pf a circle and lines RP and SP intersect each other at O.Prove that OP=OQ

Answer 1

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Answer 2

OP=OQ proved below.  

Step-by-step explanation:

Given:

Here  PQ || RS

∠OPQ = ∠ORS and ∠OQP = ∠OSR     (corresponding angles are equal)

PQRS is a cyclic quadrilateral,

Therefore, ∠OPQ = ∠OSR and ∠OQP = ∠ORS

Hence, ∠OPQ = ∠OQP

So, in triangle OPQ, ∠OPQ = ∠OQP

Therefore, OP = OQ  [property of isosceles triangle]