Question

In the given figure, a circle touches all the four side of quadrilateral ABCD with AB=6 cm, BC=7 cm and CD=4 cm. Find AD.

Answer 1

It is known that the length of the tangents drawn from an external point to the circle is equal.

$AP=AS$..............(i)

$BP=BQ$...............(ii)

$CQ=CR$..................(iii)

$DR=DS$...................(iv)

Now,

$AB+CD=\left(AP+PB\right)+\left(CR+DR\right)$

$AB+CD=\left(AS+BQ\right)+\left(CQ+DS\right)$

$AB+CD=\left(AS+DS\right)+\left(BQ+CQ\right)$

$AB+CD=AD+BC$

$AD=AB+CD-BC$

$AD=6+4-7$

$AD=3cm$