Question

In Fig. 10.100, a circle with centre O is inscribed in a quadrilateral ABCD such that, it touches sides BC, AB, AD and CD at points P, Q, R and S respectively. If AB = 29 cm, AD = 23 cm, ∠B = 90° and DS = 5 cm, then the radius of the circle (in cm) is
A. 11
B. 18
C. 6
D. 15

Answer 1

Answer:

A. 11 cm

Step-by-step explanation:

Property Used: Tangents from same external point are equal in length.

DR=DS=5 cm

AR=AQ

AR=AD-DR=23-5=18 cm

BQ=AB-AQ=29-18=11 cm

In square BPOQ

r=BQ=11 cm