Question

In the given figure ABCD is quadrilateral circumscribing a circle with centre O. If $\angle$B = ${90}^0$, AD = 23 cm, AB = 29 cm and DS = 5 cm, then the radius of the circle is ___ 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

But DR = DS = 5 cm( $\because$ Tangents drawn from an external point to a circle are equal)

$\therefore$AR = AD –DR

= 23 -5 = 18 cm

AQ = AR = 18 cm( $\because$ Tangents drawn from an external point to a circle are equal)

BQ = AB – AQ

= 29 – 18 = 11 cm

Hence r = 11 cm