Question

Quadrilateral ABCD is circumscribed to a circle. If AB = 6 cm, BC = 7 cm and CD = 4 cm then the length of AD is

(a) 3 cm (b) 4 cm (c) 6 cm (d) 7 cm

Answer 1

Sol :
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 .