Question

Find the equation of a circle with origin as centre and which circumscribes an equilateral triangle whose median is of the length $3a$.

Answer 1

If the centroid of the triangle coincides with the centre of the circle,then the radius of the circle is $\frac{2}{3}$ of the length of the median.

Therefore,

Length of median $=3a$

$\Rightarrow$ Radius of circle $=\frac{2}{3}\times 3a=2a$

Centre of circle $=(0,0)$

Therefore,

Equation of circle-

${(x-0)}^2+{(y-0)}^2={\left(2a\right)}^2$

$\Rightarrow x^2+y^2=4a^2$