2012 USAMO 第 5 题

Let $P$ be a point in the plane of triangle $ABC$, and $\gamma$ a line passing through $P$. Let $A'$, $B'$, $C'$ be the points where the reflections of lines $PA$, $PB$, $PC$ with respect to $\gamma$ intersect lines $BC$, $AC$, $AB$, respectively. Prove that $A'$, $B'$, $C'$ are collinear.

设$P$为三角形$ABC$平面上的一点，$\gamma$为穿过$P$的直线。设$A'$、$B'$、$C'$分别为线$PA$、$PB$、$PC$相对于$\gamma$的反射与线$BC$、$AC$、$AB$的交点。证明$A'$、$B'$、$C'$共线。