Construct a right triangle with given hypotenuse such that the median drawn to the hypotenuse is the geometric mean of the two legs of the triangle.
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Construct a right triangle with given hypotenuse $c$ such that the median drawn to the hypotenuse is the geometric mean of the two legs of the triangle.
Source: Međunarodna matematička olimpijada, shortlist 1959
Školjka 
such that the median drawn to the hypotenuse is the geometric mean of the two legs of the triangle.