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1987 OIM Problems/Problem 2

Revision as of 12:47, 13 December 2023 by Tomasdiaz (talk | contribs) (Created page with "== Problem == On a triangle <math>ABC</math>, <math>M</math> and <math>N</math> are the respective midpoints of sides <math>AC</math> and <math>AB</math>, and <math>P</math> i...")
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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.

Solution

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