In the given figure a circle is inscribed in a quadrilateral ABCD in which ∠B = 900. If AD = 23 cm AB = 29 cm and DS = 5 cm, find the radius of the circle in cm.
In the given fig OP⊥BC and OQ⊥BA
Also, OP = OQ =r
∴OPBQ is a square [ ∵∠B = 900 ]
∴BP = BQ =r
But DR = DS = 5 cm
∴AR = AD –DR
= 23 -5 = 18 cm
AQ = AR = 18 cm
BQ = AB – AQ
= 29 – 18 = 11 cm
Hence, r = 11 cm