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Question

A quadrilateral ABCD is drawn to circumscribe a circle Such that its sides AB, Bc, CD and AD touchs the circle at P, Q, R , and S respectively. If AB=xcm , BC=7cm, CR=3cm and As=5cm, find x


Solution

we know that :AB=x

when we draw the figure we get that AB, BC ,CD and AD are tangents to given circle .

So , x=AP+PB .............(i)

AP=AS

BP=BQ

QC=RC=3cm

BQ= 4cm

BQ=BP= 4cm

AP = AS =5cm

From (I) we get that

x= AP+BP

x= 4+5

x=9cm=AB

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