1997 CMO 第 4 题

Consider a cyclic quadrilateral $ABCD$ . The extensions of its sides $AB,DC$ meet at the point $P$ and the extensions of its sides $AD,BC$ meet at the point $Q$ . Suppose $\quad QE,QF$ are tangents to the circumcircle of quadrilateral $ABCD$ at $E,F$ respectively. Show that $P,E,F$ are collinear.

考虑一个循环四边形 $ABCD$ 。其边 $AB,DC$ 的延伸在点 $P$ 处相交，其边 $AD,BC$ 的延伸在点 $Q$ 处相交。假设$\quad QE,QF$分别与四边形$ABCD$的外接圆在$E,F$处相切。证明 $P,E,F$ 共线。