UKMT Intermediate Mathematical Challenge, 2016

A Saxon silver penny, from the reign of Ethelbert II in the eighth century, was sold in 2014 for £78 000. A design on the coin depicts a circle surrounded by four equal arcs, each a quarter of a circle, as shown. The width of the design is 2 cm. What is the radius of the small circle, in centimetres?

(A) $\frac{1}{2}$ (B) $2 - \sqrt{2}$ (C) $\frac{1}{2}\sqrt{2}$ (D) $5 - 3\sqrt{2}$ (E) $2\sqrt{2} - 2$