Question

1.A circle touches all four sides of a quad ABCD whose sides are AB=6cm BC=9cm CD=8cm. Find the length of side AD.

Answer 1

Let the circle touch the quad. ABCD at P,Q,R,S on sides AB,BC,CD,AD respectively...then,

since A,B,C,D are external points through which tangents are drawn, the,

AP = AS

BP = BQ

CR = CQ

DR = DS...

adding LHS and RHS, we get,

AP + BP+ CR+DR = AS + DS+BQ + CQ

6 + 8 = AS+DS + 9 ....(since AP+BP = 6, CR +DR = 8 and BQ+CQ= 9)

14-9 = AD

so, AD = 5cm.