Question

7.) In the given figure, a circle touches all the four sides of a
quadrilateral ABCD, whose three sides AB = 8 cm,
BC = 9 cm and CD = 6 cm. Find AD.​

Answer 1

Answer:

We know, tangents from an external point to a circle are always equal.

Therefore, AP = AS, BP = BQ, CR = CQ and DR = DS

Now from figure, AP + BP + CR + DR = AS + BQ + CQ + DC

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

AB + CD = AD + BC

8+ 6= AD + 9

AD = 5cm