1991 OIM Problems/Problem 6

Problem

Given 3 non-aligned points $M$ , $N$ and $H$ , we know that $M$ and $N$ are midpoints of two sides of a triangle and that $H$ is the point of intersection of the heights of said triangle. Build the triangle.

~translated into English by Tomas Diaz. ~orders@tomasdiaz.com

Solution

Case 1: $\angle NHM = 90^{\circ}$

If you measure the angle $\angle NHM$ on teh given points and it happens to be a right angle, then

Note. I actually competed at this event in Argentina when I was in High School representing Puerto Rico. I think I may have been able to build some cases of this. I don't remember much of it.

Alternate solutions are always welcome. If you have a different, elegant solution to this problem, please add it to this page.

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1991 OIM Problems/Problem 6

Problem

Solution

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