1987 OIM Problems/Problem 2

Problem

On a triangle $ABC$, $M$ and $N$ are the respective midpoints of sides $AC$ and $AB$, and $P$ is the midpoint of the intersection of $BM$ and $CN$. Prove that, if is possible to inscribe a circumference in the quadrilateral $ANPM$, then triangle $ABC$ is isosceles.

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

Solution

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See also

https://www.oma.org.ar/enunciados/ibe2.htm