Question

Origin is the center of circle passing through the vertical of an equilateral triangle whose median is of length 3a then equation of the circle is

• A. $x^2+y^2=a^2$
• B. $x^2+y^2={2a}^2$
• C. $x^2+y^2={3a}^2$
• D. $x^2+y^2={4a}^2$

Answer 1

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

Equation of a circle passing through the origin is $x^2+y^2=a^2$.

Now,

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.

Hence $r=\frac{2}{3}\times 3a$

$⟹r^2=4a^2$

Hence the equation of the circle is $x^2+y^2=4a^2$