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)