Question

A circle touches all the four sides of a quadilateral abcd with sides ab = 6 bc=7 and cd= 4.find ad

Answer 1

Solution :

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

ΣAP + BP + CR + DR = AS + BQ + CQ + DS
AB + CD = AD + BC
6 + 4 = AD + 7
AD = 3