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 $\Delta A B C=9$

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