Question

A circle touches all the four sides of a quadrilateral ABCD whose sides are AB = 6 cm , BC = 7 cm and CD = 4 cm. 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
6 + 4 = AD + 7
AD = 3 cm .

Answer 2

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