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CBSE Class 10 Answered

If PA and PB are two tangents drawn from a point P to a circle with centre O touching it at A and B, prove that OP is perpendicular bisector of AB.
Asked by Topperlearning User | 05 Oct, 2017, 10:32: AM
answered-by-expert Expert Answer
Let PO intersect AB at a point C.
In begin mathsize 12px style increment end styleACP and begin mathsize 12px style increment end styleBCP,
AP = BP         (Tangents from an external point are equal)
PC = PC         (Common side)
APO = BPO
(Tangents from an external point are equally inclined to the line joining this point to the centre)
Therefore begin mathsize 12px style increment end styleACP begin mathsize 12px style increment end styleBCP             (SAS criterion)
AC = CB                                    (CPCT)
ACP= BCP = begin mathsize 12px style 1 half end style180o = 90o (CPCT)
Hence OP is the perpendicular bisector of AB.
Answered by | 05 Oct, 2017, 12:32: PM
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