Question

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

Answer 1

In the given figure,

A circle touches all the four sides of a quadrilateral $ABCD$ whose sides are $AB=6cm,BC=9cm$ and $CD=8cm$

Let $P,Q,R$ and $S$ are points where circle touches the sides $AB,BC,CD$ and $DA$ respectively.

Therefore,

$AB+CD=BC+AD$

$6+8=9+AD$

$14=9+AD$

$AD=14-9=5$

Length of $AD$ is $5cm.$