Question

In the following figure, a circle touches all the four sides of a quadrilateral ABCD. If AB = 6 cm, BC = 9 cm and CD = 8 cm, then find the length of AD.

Answer 1

Here, AP = AS   ...[Tangents drawn from an external point to a circle are equal in length]

Let AP = AS = x

Similarly, BP = BQ, CQ = CR and RD = DS

Since, AP = x

⇒ BP = AB – AP

= 6 – x   ...[∵ AB = 6 cm]

Now, BP = BQ

= 6 – x

⇒ CQ = BC – BQ

= 9 – (6 – x)   ...[∵ BC = 9 cm]

= 3 + x

Now, CQ = CR

= 3 + x

⇒ RD = CD – CR

= 8 – (3 + x)   ...[∵ CD = 8 cm]

= 5 – x

Now, RD = DS

= 5 – x

⇒ AD = AS + SD

= x + 5 – x

= 5

∴ AD = 5 cm.