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

• A. $\frac{5π}{18}$
• B. $\frac{6π}{25}$
• C. $\frac{3π}{25}$
• D. $\frac{2π}{15}$

Answer 1

Answer: (B)

$\frac{6π}{25}$

Answer 2

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) ⊥ $DC$.
Also $DC = \sqrt{6^2+8^2} = 10$
As area of $ΔODC$ should be the same, we have,$\frac{1}{2}×6×8=\frac{1}{2}×OE×10$
$⇒ OE = 4.8$
$∴$ Required ratio of areas = $\frac{π(4.8)^2}{\frac{1}{2}×12×16} = \frac{6π}{25}$

So, the correct answer is (B): $\frac{6π}{25}$