1991 OIM Problems/Problem 6

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Problem

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

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

Solution

  • 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.

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See also

https://www.oma.org.ar/enunciados/ibe6.htm