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Question

In the given figure, the circle touches the sides AB,BC,CD,DA of a quadrilateral ABCD at the points P,Q,R,S respectively. If AB=11cm,BC=xcm,CR=4cm,AS=6cm, then the value of x is
239532_58dcdda2326143c281f42b6560dd03eb.png

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Solution

GivenABCDisaquadrilateral,inscribingacirclewhichtouchesABatP,BCatQandDCatRandADatS.AS=6cm,AB=11cm,CR=4cmandBC=xcm.Tofindoutx=?SolutionWeknowthatthelengthsofthetangents,fromapointtoacircle,areequal.CR=CQ=4cm,AS=AP=6cmandBP=BQ.NowBP=ABAP=(116)cm=5cm.BQ=BP=5cm.BC=x=BQ+CQ=(5+4)cm=9cm.AnsOptionA.

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