Question

An equilateral triangle has two vertices (-2,0) and (2,0) and its third vertex lies below the x-axis, the equation of the circumcircle of the triangle is

• A.
• B.
• C.
• D.

Answer 1

The correct option is D

ABC is an equivlateral triangle.
So we get $C=(0,-2\sqrt{3})$
Centroid of $\Delta ABC=(0,\frac{-2}{\sqrt{3}})$

Therefore radius of circumcircle $=\sqrt{(2{)}^2+{\left(\frac{2}{\sqrt{3}}\right)}^2}$
$=\frac{4}{\sqrt{3}}$
Equation of circle is $(x-0{)}^2+{(4+\frac{2}{\sqrt{3}})}^2={\left(\frac{4}{\sqrt{3}}\right)}^2$
$\sqrt{3}(x^2+y^2)+4y-4\sqrt{3}=0$