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
Expert Answer
Let PO intersect AB at a point C.
In ACP and BCP,
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 ACP BCP (SAS criterion)
AC = CB (CPCT)
ACP= BCP = 180o = 90o (CPCT)
Hence OP is the perpendicular bisector of AB.
Answered by | 05 Oct, 2017, 12:32: PM
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