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Question

Prove that the tangent at the extremities of any chord makes equal angles at the chord.

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Solution


Let AB be a chord of a circle with centre O, and let AP and BP be the tangents at A and B respectively.

Suppose the tangents meet at P. Join OP. Suppose OP and meets AB at C.

We have to prove that PAC=PBC.

In triangle PCA and PCB, we have

PA=PB [ tangents from an external point are equal]
APC=BPC [PA and PB are equal inclined to OP].
PC=PC

So, by SAScriterion of congruence, we have

PACPBC
PAC=PBC

1031485_1009631_ans_5558c2aaf92345919e94286877aa590a.png

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