In the adjoining figure, a circle touches all the four sides of a quadrilateral ABCD whose sides are AB=6cm, BC=9cm and CD=8 cm. Find the length of side AD.

Sol:

We know that when a quadrilateral circumscribes a circle then sum of opposites sides is equal to the sum of other opposite sides.

\ AB + CD = AD + BC

Þ 6 + 8 = AD = 9

Þ AD = 5 cm