Question

A circle touches all the sides of [] ABCD. If AB is the largest side then prove that CD is the smallest side. ​

Answer 1

Answer:

Given that a circle touches all the sides of ABCD and AB is the largest side.

We have to prove that CD is the smallest side.

Proof:

The circle touches all sides of ABCD.

∴ AB + CD = BC + DA … (1)

Given AB is the largest side.

⇒ AB > BC

∴ AB = BC + m

From (1),

⇒ BC + m + CD = BC + DA

⇒ CD + m = DA