The vertices of a triangle are (0,0),(4,0) and (3,9). The ar... | Quantitative Aptitude | SolveeIt

The vertices of a triangle are (0,0),(4,0) and (3,9). The area of the circle passing through these three points is

$\frac{14π}{3}$

$\frac{12π}{5}$

$\frac{123π}{7}$

$\frac{205π}{9}$

Answer

$\frac{205π}{9}$

Explanation

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

Area of the triangle = $\frac{1}{2}×4×9=18$

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

Area of the circle = $πR^2 = π\bigg(\frac{abc}{4Δ}\bigg) = \frac{π(4.\sqrt{90}.\sqrt{82})^2}{(4.18)^2}$

= $π×\frac{16×90×82}{16×18×18} = \frac{205}{9}π$

So, the correct answer is (D): $\frac{205π}{9}$

Quantitative Aptitude Question on Mensuration