# Area of the largest square inscribed in an equilateral triangle that is itself inscribed in a circle of radius $r$

$\triangle ABC$ is an equilateral triangle inscribed in a circle of radius $r$. What is the area of the largest square that can be inscribed inside it?

My doubt: How side of an equilateral triangle will be $r\sqrt{ 3}$

• Do you know how to solve further if you get $a=r\sqrt 3$? – Jaideep Khare Aug 1 '17 at 20:59
• Yes @JaideepKhare – EmilySekuz Aug 1 '17 at 21:04

$\angle OBC = 30^\circ$, Hence $BM=r\cos 30^\circ = \frac{\sqrt3 r}{2}.$
Task given to you, find the length of $BC$.