Question

A circle having centre at the origin passes through the three vertices of an equilateral triangle the length of its median being $9$ units. Then the equation of that circle is

• A. $x^2+y^2=9$
• B. $x^2+y^2=18$
• C. $x^2+y^2=36$
• D. $x^2+y^2=81$

Answer 1

Answer: (C)

Given length of median of $\Delta ABC=9$

$\therefore AO=\frac{2}{3}AD$
$AO=\frac{2}{3}\times 9=6$
$O$ is the circumcentre of $\Delta ABC$.
We know that in equilateral triangle circumcentre incentre, centroid coincide.
$\therefore AO$ is radius of circle.
Hence, equation of circle is
$x^2+y^2=6^2\Rightarrow x^2+y^2=36$