Question

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

Answer 1

Given:

A circle touches all four sides of the quadrilateral ABCD with sides AB = 6 cm, BC = 7 cm, and CD = 4 cm. We need to find AD.

Step 1: Property of a tangential quadrilateral (a quadrilateral that has an incircle touching all four sides):

The sum of the lengths of the opposite sides is equal. Thus, AB + CD = BC + AD

Step 2: Substitute the known values: 6 + 4 = 7 + AD

Step 3: Simplify the equation: 10 = 7 + AD

Step 4: Solve for AD: AD = 10 − 7 = 3 cm

AD = 3 cm