1967 AHSME Problem 3

The side of an equilateral triangle is s. A circle is inscribed in the triangle and a square is inscribed in the circle. The area of the square is:

\text{(A)}\ \frac{s^2}{24}\qquad\text{(B)}\ \frac{s^2}{6}\qquad\text{(C)}\ \frac{s^2\sqrt{2}}{6}\qquad\text{(D)}\ \frac{s^2\sqrt{3}}{6}\qquad\text{(E)}\ \frac{s^2}{3}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.