Question

In the given figure, a circle touches all the four sides of a quadrilateral ABCD whose three sides are AB = 6cm, BC=7cm and CD=4 cm. Find AD.

Answer 1

Let the circle touch the sides of the quadrilateral AB, BC, CD and DA at P, Q, R and S respectively.

Given, AB = 6cm, BC = 7 cm and CD = 4cm.
Tangents drawn from an external point are equal.
∴ AP = AS, BP = BQ,CR = CQ and DR = DS
Now, AB + CD (AP + BP) + (CR + DR)

⇒AB + CD= (AS+ BQ) + (CQ+ DS)

 ⇒ AB +CD +(AS+ DS) +(BQ+ CQ)
⇒ AB +CD =AD+ BC
⇒AD= ( AB+ CD)- BC
⇒ AD=(6+4)-7
⇒ AD = 3 cm.
∴ The length of AD is 3 cm.