A circle is inscribed in an equilateral triangle of side a, the area of any square inscribed in the circle is
If p be the altitude, then p = asin 60∘ = a2√.
Since the triangle is equilateral, therefore centroid, orthocentre, circumcentre and incentre all coincide.
Hence, radius of the inscribed circle = 13p=a2√=r or diameter=2r=a√.
Now if x be the side of the square inscribed, then angle in a semicircle being a right angle, hence
So the area of the square is x2=a26