Q) In the given figure, a circle is inscribed in a quadrilateral ABCD in which ∠B = 90⁰. If AD = 17 cm, AB = 20 cm and DS = 3 cm, then find the radius of the circle.

Ans:

In the above diagram, DR = DS = 3 cm

Therefore, AR = AD – DR = 17 – 3 = 14 cm

⇒AQ = AR = 14 cm

⇒QB = AB – AQ = 20 – 14 = 6 cm

Since QB = OP = r,

Therefore radius r = 6 cm