Question

In the adjoing figure, a circle touches all the four sides fo a quadrilateral ABCD whose sides are AB = 6 cm, BC = 9 cm and CD = 8 cm. Find the length side AD.

Answer 1

ABCD is a quadrilateral. A circle touches the sides AB, BC, CD and DA of the quadrilateral ABCD at P, Q, R and S respectively

.AB = 6 cm, CD = 8 cm and BC = 9 cm
We know that, the length of tangents drawn from an external point to the circle are equal.
AP = AS
BP = BQ
CQ = CR
DR = DS
Now, AB + CD = (AP + PB) + (CR + DR)
= (AS + BQ) + (CQ + DS)
= (AS + DS) + (BQ + CQ)
= AD + BC
∴ AB + CD = AD + BC
⇒ AD = AB + CD – BC
⇒ AD = 6 cm + 8 cm – 9 cm
⇒ AD = 14 cm – 9 cm
⇒ AD = 5 cm
Thus, the length of the side AD is 5 cm.