AHSME 1967 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: $\text{(A)}\ \frac{s^2}{24} \text{(B)}\ \frac{s^2}{6} \text{(C)}\ \frac{s^2\sqrt{2}}{6} \text{(D)}\ \frac{s^2\sqrt{3}}{6} \text{(E)}\ \frac{s^2}{3}$