Question

28. In Fig. 8.104, 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 respectively. If AB = 29 cm,
AD - 23 cm, ZB=90° and DS = 5 cm, then the radius of the circle (in cm) is
A
R
S
с
P
B
Fig. 8.104​

Answer 1

DR = DS (Tangent from same external point)

DR = 5 cm

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

AR = AQ (Tangent from same external point)

AQ = 18 cm

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

OPBQ is a square , therefore r = 11 cm