IMO 1959 Problem 04

The year is 1959. The place: Braşov, Romania, where the first International Mathematical Olympiad is being held. The problem is short, simple and sweet:

Construct a right-angled triangle whose hypotenuse c is given if 
it is known that the median from the right angle equals the 
geometric mean of the remaining two sides of the triangle.

The mathematical solution is left as an exercise, because you can use the brute force Luke. :D

Cheers.