CAT 2020 Slot 3 QA Question 13: The vertices of a triangle are $(0,0)$, $(4,0)$ and $(3,9)$. The area of the circle passing through these three points is

Question

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

Accepted Answer

Use the circumradius formula $R = \dfrac{abc}{4\Delta}$, where $a$, $b$ and $c$ are the side lengths and $\Delta$ is the area of the triangle.
Side lengths are $4$, $\sqrt{82}$ and $\sqrt{90}$.
Area of triangle = $\Delta = \dfrac{1}{2} 	imes 4 	imes 9 = 18$
$R^2 = \dfrac{4^2 	imes 82 	imes 90}{1

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

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