Question

a circle touches all the four sides of a quadrilateral ABCD with 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 = DSAdding AP + BP + CR + DR = AS + BQ + CQ + DS AB + CD = AD + BC 6 + 4 = AD + 7AD = 3 cm .