Question

A circle passes through the three vertices of an equilateral triangle that has sides of length $3$. The area of the circle is -

• A. $\frac{9\pi }{4}$
• B. $3\pi$
• C. $\frac{27\pi }{16}$
• D. $\frac{5\pi }{2}$

Answer 1

Answer: (B)

$3\pi$

O is the center of the circle and also centroid of $△ABC$

$AD$ is the median and its length is $A{D}^2=3^2–(\frac{3}{2}{)}^2=\frac{3\sqrt{3}}{2}$

Centroid divides median in 2:1 ratio

$AO=\frac{2}{3}AD=\sqrt{3}=radiusofthecircle$

Area = $\pi r^2=3\pi$