CAT 2020 Slot 1 QA Question 14: A circle is inscribed in a rhombus with diagonals 12 cm and 16 cm. The ratio of the area of the circle to the area of the rhombus is

Question

A circle is inscribed in a rhombus with diagonals 12 cm and 16 cm. The ratio of the area of the circle to the area of the rhombus is

Accepted Answer

The diagonals of a rhombus bisect each other at right angles. So the side of the rhombus is found using half-diagonals 6 and 8.

Side = $\sqrt{6^2 + 8^2} = 10$ cm

Area of rhombus = $\dfrac{1}{2} 	imes 12 	imes 16 = 96$
Semiperimeter = $\dfrac{4 	imes 10}{2} = 20$

For a tangential quadrilateral,