Question

The equation of a circle with origin as a centre and passing through equilateral triangle whose median is of length 3a is

• A. $x^2+y^2={9a}^2$
• B. $x^2+y^2={16a}^2$
• C. $x^2+y^2={4a}^2$
• D. $x^2+y^2=a^2$

Answer 1

The correct option is C $x^2+y^2={4a}^2$

$AD$ is the medium, $0$ is centroid.

$\because {△}^{le}$ is equilateral

$\therefore 0$ is also the circumcentre

$\therefore$ radius of circle $=OA$

$=\frac{2}{3}AD$

$=2a$

$\therefore$ equation of circle $=x^2+y^2=4a^2$

Hence, the answer is $x^2+y^2=4a^2.$