Q. 105.0( 8 Votes )

In the given figure, ABCD is a quadrilateral in which D=90°. A circle C (O,r) touches the sides AB, BC, CD and DA at P,Q,R,S respectively, If BC =38 cm, CD=25 cm and BP=27 cm, find the value of r.


Answer :

r is the radius which is OR = r


Consider quadrilateral DROS


RDS = 90° …given


DRO = 90° …radius is perpendicular to the tangent


DR = DS …tangents drawn from the same point are equal


As the adjacent angles are 90° and adjacent sides are same hence DROS is a square


Hence OR = DR = r …(i)


As tangents drawn from the same point are equal


BQ and BP are tangents drawn from B


BQ = BP
BQ = 27 cm …BP is 27 cm given


From figure


BC = BQ + QC


38 = 27 + QC …BC is 38 cm given


QC = 11 cm


CQ and CR are tangents drawn from C


CQ = CR …tangents from same point


CR = 11 cm


Again from figure


CD = CR + RD


25 = 11 + r …CD is 25 given and RD = r from (i)


r = 14 cm


Hence r radius is 14 cm


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