# CAT 2020 Quant Question [Slot 1] with Solution 21

Question

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

1. $\frac{{5\pi }}{{18}}$
2. $\frac{{6\pi }}{{25}}$
3. $\frac{{3\pi }}{{25}}$
4. $\frac{{2\pi }}{{15}}$
Option: 2
Solution:

Given the circle is inscribed in the rhombus of diagonals 12 and 16 . Let O be the point of intersection of the diagonals of the rhombus. Then, OE (radius) $\bot$ DC.

Also $DC = \sqrt {{6^2} + {8^2}} = 10$

As area of $\Delta ODC$ should be the same, we have, $\frac{1}{2} \times 6 \times 8 = \frac{1}{2} \times OE \times 10$

$\Rightarrow OE = 4.8$

$\therefore$ Required ratio of areas $= \frac{{\pi {{(4.8)}^2}}}{{\frac{1}{2} \times 12 \times 16}} = \frac{{6\pi }}{{25}}$

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