Question

In the given fig. a circle is inscribed in a quadrilateral ABCD in which $\angle$B = ${90}^0$. If AD = 23 cm AB = 29 cm and DS = 5 cm, find the radius of the circle (in cm).

Answer 1

In the given fig OP$\perp$BC and OQ$\perp$BA

Also, OP = OQ =r

$\therefore$OPBQ is a square [ $\because$∠B = ${90}^0$ ]

$\therefore$BP = BQ =r (1 mark)

But DR = DS = 5 cm

$\therefore$AR = AD –DR

= 23 -5 = 18 cm (0.5 mark)

AQ = AR = 18 cm

BQ = AB – AQ

= 29 – 18 = 11 cm (0.5 mark)

Hence r = 11 cm