Question

A circle touches all the sides of quadrilateral ABCD . If AB=8, BC=10 & CD=7, then 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
8 + 7 = AD + 10
AD = 5 cm .