cat 2020 Question 18

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

Let the length of radius be ‘$r$’.

From the above diagram,

$x^2 +r^2 = 6^2$ ....(i)

$(10 - x)^2 + r^2 = 8^2$ ....(ii)

Subtracting (i) from (ii), we get:

$x = 3.6$ => $r^2 = 36 - (3.6)^2$ = $23.04$ ==> $r^2 = 36 - (3.6)^2$ = $23.04$

Area of circle = $\pi r^2 = 23.04 \pi$

Area of rhombus = 1/2*d1*d2 = 1/2*12*16 = 96.

.’. Ratio of areas = 23.04$\pi$ / 96 = $\frac{6 \pi}{25}$

Question 18.