Square $$ABCD$$ is inscribed in a circle. Square $$EFGH$$ has vertices $$E$$ and $$F$$ on $$\overline{CD}$$ and vertices $$G$$ and $$H$$ on the circle. The ratio of the area of square $$EFGH$$ to the area of square $$ABCD$$ can be expressed as $$\frac {m}{n}$$ where $$m$$ and $$n$$ are relatively prime positive integers and $$m < n$$. Find $$10n + m$$.

(第十九届AIME2 2001 第6题)