Question

Two equal circles intersect in P and Q. A straight line through P meets the circle in A and B . Prove that QA=QB

Answer 1

since the circles are equal, their radii will also be equal. here, QA and QB are radii. therefore
QA=QB

Answer 2

Proof:

Since PQ is the common cord of the circle

Therefore,

arc PQ of 1st circle = arc PQ of 2nd circle

Therefore,

∠PAQ = ∠PBQ

In ΔQAB

∵ ∠PAQ = ∠PBQ

∴ QA = QB   (In a triangle, sides opposite to the equal angles are equal)

(Proved)

Hope this helps.

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