1991 IMO 第 1 题

(PHI 3) Let $A B C$ be any triangle and $P$ any point in its interior. Let $P_{1}, P_{2}$ be the feet of the perpendiculars from $P$ to the two sides $A C$ and $B C$. Draw $A P$ and $B P$, and from $C$ drop perpendiculars to $A P$ and $B P$. Let $Q_{1}$ and $Q_{2}$ be the feet of these perpendiculars. Prove that the lines $Q_{1} P_{2}, Q_{2} P_{1}$, and $A B$ are concurrent.

(PHI 3) 设 $A B C$ 为任意三角形，$P$ 为其内部的任意点。令$P_{1}、P_{2}$ 为从$P$ 到两条边$A C$ 和$B C$ 的垂线的脚。绘制$A P$ 和$B P$，并从$C$ 垂线垂直于$A P$ 和$B P$。令 $Q_{1}$ 和 $Q_{2}$ 为这些垂线的脚。证明 $Q_{1} P_{2}、Q_{2} P_{1}$ 和 $A B$ 行是并发的。