Question

In the given figure, a circle touches all the four sides of a quadrilateral $ABCD$ whose sides $AB=6cm,BC=7cm$ and $CD=4cm$, find $AD$.

Answer 1

Let $P,Q,R,S$ be the points where the circle touches the quadrilateral .From a point out side of the circle the two tangents to the circle are equal.
$AP=AS$, $BP=BQ$ , $CR=CQ$ and $DR=DS$
Adding $AP+BP+CR+DR=AS+BQ+CQ+DS$
$AB+CD=AD+BC$
$6+4=AD+7$
$AD=3cm$.