Please submit your concern

Explanation:

The following diagram can be drawn from the given information.

​​​​​​​

⇒ Area of the Rhombus = $\frac{1}{2}\times 12\times 16$ = 96

Radius of the circle is same as the height of ∆ABC

In a right triangle, altitude from right angle = $\frac{Product of shorter sides}{hypotenuese}$ = $\frac{\left(6\times 8\right)}{10}$ = $\frac{24}{5}$

⇒ Area of circle = $\pi {\left(\frac{24}{5}\right)}^2$

∴ Area of Circle : Area of Rhombus = $\pi {\left(\frac{24}{5}\right)}^2 : 96$ = 6π : 25.

Hence, option (d).