Question

The equation of a circle with the origin as the centre and passing through the vertices of an equilateral triangle whose altitude is of length $3$ units is

• A. $x^{2}+y^{2}=9$
• B. $x^{2}+y^{2}=16$
• C. $x^{2}+y^{2}=4$
• D. $x^{2}+y^{2}=1$

Answer 1

Answer: (C)

Circle circumscribes the triangle $ABC$ and has center at $\left(0 , 0\right)$ .
$AD=3$
$\therefore OA=\frac{2}{3}\times 3=2$
$\therefore $ radius of circle, $OA=2$
Thus, equation of circle is $x^{2}+y^{2}=4$