CAT 2020 Slot 1 QA Q18 Geometry

Question 18 of the Quantitative Ability (QA) section, CAT 2020 Slot 1, with CAT's official answer and a worked solution.

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

A
\(\frac{2π}{15}\)
B
\(\frac{6π}{25}\)
C
\(\frac{3π}{25}\)
D
\(\frac{5π}{18}\)

Answer: (B) (6π)/25 Geometry MCQ

Solution

Half-diagonals 6 and 8, so side = 10 and area \(= \frac{12\times16}{2} = 96\).
Inradius = height / 2 = \(\frac{96}{10\times2} = 4.8\).
Ratio \(= \frac{\pi(4.8)^2}{96} = \frac{23.04\pi}{96} = \frac{6\pi}{25}\).