# 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.

r is the radius which is OR = r

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

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Quiz | Imp. Qs. on Circle35 mins
Quiz | Imp. Qs. on Circles37 mins
Quiz | Testing Your Knowledge on Circles32 mins
Short Cut Trick to Find Area of Triangle43 mins
Quiz | Areas Related to Circles43 mins
RD Sharma | Area of Sector and Segments25 mins
Quiz | Area Related with Circles47 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses