Question

circle touches all side of square ABCD if AB= 7 BC=10 and CD= 8 then 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 .

AD=3cm.