2006 USAMO 第 6 题

Let $ABCD$ be a quadrilateral, and let $E$ and $F$ be points on sides $AD$ and $BC$, respectively, such that $AE/ED = BF/FC$. Ray $FE$ meets rays $BA$ and $CD$ at $S$ and $T$ respectively. Prove that the circumcircles of triangles $SAE$, $SBF$, $TCF$, and $TDE$ pass through a common point.

设$ABCD$为四边形，$E$和$F$分别为边$AD$和$BC$上的点，使得$AE/ED = BF/FC$。射线$FE$分别在$S$和$T$处与射线$BA$和$CD$相遇。证明三角形 $SAE$、$SBF$、$TCF$ 和 $TDE$ 的外接圆通过公共点。