1960 IMO 第 6 题

An isosceles trapezoid with bases $a$ and $b$ and height $h$ is given. (a) On the line of symmetry construct the point $P$ such that both (nonbase) sides are seen from $P$ with an angle of $90^{\circ}$. (b) Find the distance of $P$ from one of the bases of the trapezoid. (c) Under what conditions for $a, b$, and $h$ can the point $P$ be constructed (analyze all possible cases)?

给出一个等腰梯形，底边为 $a$ 和 $b$，高度为 $h$。 (a) 在对称线上构造点 $P$，使得从 $P$ 可以看到两侧(非底边)的角度为 $90^{\circ}$。 (b) 求 $P$ 到梯形底边之一的距离。 (c) $a、b$、$h$在什么条件下可以构造点$P$(分析所有可能的情况)？