1960 IMO Problems/Problem 7

Problem

An isosceles trapezoid with bases $a$ and $c$ and altitude $h$ is given.

a) On the axis of symmetry of this trapezoid, find all points $P$ such that both legs of the trapezoid subtend right angles at $P$ ;

b) Calculate the distance of $P$ from either base;

c) Determine under what conditions such points $P$ actually exist. Discuss various cases that might arise.

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1960 IMO (Problems)
Preceded by Problem 6	1 • 2 • 3 • 4 • 5 • 6	Followed by Last Question