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  4. The equation of the circle with origin as centre passing the vertices of an equilateral triangle whose median is of length 3a is

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Q. The equation of the circle with origin as centre passing the vertices of an equilateral triangle whose median is of length $3a$ is

UPSEEUPSEE 2012

Solution:

Centre $(0,0)$, radius $=3 a \times \frac{2}{3}=2 a$
Hence, circle $x^{2}+y^{2}=4 a^{2}$ as centroid divides
median in the ratio of $2: 1$.