In trapezoid \(ABCD\), leg \(\overline{BC}\) is perpendicular to bases \(\overline{AB}\) and \(\overline{CD}\), and diagonals \(\overline{AC}\) and \(\overline{BD}\) are perpendicular. Given that \(AB=\sqrt{11}\) and \(AD=\sqrt{1001}\), find \(BC^2\).

(第十八届AIME2 2000 第8题)