Question

A,B,C,D is a quadrilateral triangle such that all of its sides touch a circle.If AB=6cm,BC=6.5cm and CD=7cm,then the length of AD is???

Answer 1

Answer:

Let P,Q,R and S be the points where the circle touches the quadrilateral. We know that the lengths of the two tangents drawn from an exterior point to a circle are equal.

Thus, we have, AP=AS,BP=BQ,CR=CQ and DR=DS.

Hence, AP+BP+CR+DR=AS+BQ+CQ+DS

⇒AB+CD=AD+BC.

⇒AD=AB+CD−BC

=6+7−6.5=6.5

Thus, AD=6.5 cm.