The conversation between human and AI assistant.
What is the area of a square inscribed in a circle, which in turn is inscribed in an equilateral triangle of side 'a'?
Yes, please.
We start by finding the radius of the circle, which is equal to the apothem of the equilateral triangle. This is r = a/(2√3). Then, we can find the side of the square, which is equal to 2r. This is s = a/√3. Finally, the area of the square is s^2 = (3-a^2)/12 * a^2.