Given−ABCDisaquadrilateral,inscribingacirclewhichtouchesABatP,BCatQandDCatRandADatS.AS=6cm,AB=11cm,CR=4cmandBC=xcm.Tofindout−x=?Solution−Weknowthatthelengthsofthetangents,fromapointtoacircle,areequal.∴CR=CQ=4cm,AS=AP=6cmandBP=BQ.NowBP=AB−AP=(11−6)cm=5cm.∴BQ=BP=5cm.∴BC=x=BQ+CQ=(5+4)cm=9cm.Ans−OptionA.