CAT 2020 Quant Question [Slot 3] with Solution 15

\(a = 4,b = \sqrt {90} ;c = \sqrt {82} \)

Area of the triangle \( = \frac{1}{2} \times 4 \times 9 = 18\)

The circumradius of the triangle \((R) = \frac{{abc}}{{4\Delta }}\)

Area of the circle \( = \pi {R^2} = \pi {\left( {\frac{{abc}}{{4\Delta }}} \right)^2} = \frac{{\pi {{(4 \cdot \sqrt {90}  \cdot \sqrt {82} )}^2}}}{{{{(4 \cdot 18)}^2}}}\)

\( = \pi  \times \frac{{16 \times 90 \times 82}}{{16 \times 18 \times 18}} = \frac{{205}}{9}\pi \)