UKMT Intermediate Mathematical Challenge, 2016

The circle has radius 1 cm. Two vertices of the square lie on the circle. One edge of the square goes through the centre of the circle, as shown. What is the area of the square?

(A) $\frac{4}{5}\text{ cm}^2$ (B) $\frac{\pi}{5}\text{ cm}^2$ (C) $1\text{ cm}^2$ (D) $\frac{\pi}{4}\text{ cm}^2$ (E) $\frac{5}{4}\text{ cm}^2$