2013 APMO 第 5 题

Let $A B C D$ be a quadrilateral inscribed in a circle $\omega$, and let $P$ be a point on the extension of $A C$ such that $P B$ and $P D$ are tangent to $\omega$. The tangent at $C$ intersects $P D$ at $Q$ and the line $A D$ at $R$. Let $E$ be the second point of intersection between $A Q$ and $\omega$. Prove that $B, E, R$ are collinear.

令$A B C D$ 为圆$\omega$ 内接的四边形，并令$P$ 为$A C$ 延长线上的一点，使得$P B$ 和$P D$ 与$\omega$ 相切。 $C$ 处的切线与 $P D$ 相交于 $Q$，线 $A D$ 相交于 $R$。令$E$ 为$A Q$ 和$\omega$ 之间的第二个交点。证明$B、E、R$共线。