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Among two mono-centered circles, AB and AC chords of the greater circle have touched the smaller circle at P and Q points respectively. Prove that PQ=½BC.

Among two mono-centered circles, AB and AC chords of the greater circle have touched the smaller circle at P and Q points respectively. Prove that PQ=½BC.

Grade:10

1 Answers

Aditya Gupta
2081 Points
4 years ago
mono centered circles means concentric circles with a common centre, say O
now, consider chord AB of the greater circle touching the smaller circle at P. this means that AB is a tangent to the smaller circle at P, so that OP is perpendicular to AB. this also means that P bisects chord AB of the greater circle (from perpendicular chord theorem). 
similarly Q bisects AC. applying mid point theorem in triangle ABC, we conclude that PQ= ½BC
kindly approve :)

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