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Question

In figure AB is a chord of length 16cm of a circle of radius 10cm. The tangents at A andB intersect at a point P. Find the length of PA.
772889_a288b558e5504084a488856e1ea565e3.PNG

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Solution

given Radius of circle =r=BO=10cm
AB=16cm
PBO=90 ......Property of Tangent to circle
Property : A pair of tangents drawn from external point to circle are Equal and subtend 90 at he centre.

PA=PB

OP perpendicularly bisects AB at M Please mark on figure .

BM=MA=8cm

Considering the triangle ΔBOM

sin(MOB)=sin(POB)=810

tan(POB)=86

Considering the triangle ΔPOB

tan(POB)=PBBO=86


PB10=86

PA=PB=403cm

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