2022 IMO Shortlist G6

In an acute-angled triangle $A B C$, point $H$ is the foot of the altitude from $A$. Let $P$ be a moving point such that the bisectors $k$ and $\ell$ of angles $P B C$ and $P C B$, respectively, intersect each other on the line segment $A H$. Let $k$ and $A C$ meet at $E$, let $\ell$ and $A B$ meet at $F$, and let $E F$ and $A H$ meet at $Q$. Prove that, as $P$ varies, the line $P Q$ passes through a fixed point. (Iran)

在锐角三角形 $A B C$ 中，点 $H$ 是从 $A$ 开始的高度的底脚。设$P$为移动点，使得角$P B C$和$P C B$的平分线$k$和$\ell$分别在线段$A H$上彼此相交。让$k$和$A C$在$E$相遇，让$\ell$和$A B$在$F$相遇，让$E F$和$A H$在$Q$相遇。证明，当 $P$ 变化时，线 $P Q$ 通过一个固定点。 (伊朗)