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1989 OIM Problems/Problem 4

Revision as of 13:20, 13 December 2023 by Tomasdiaz (talk | contribs) (Created page with "== Problem == The circumference inscribed in triangle <math>ABC</math>, is tangent to sides <math>AB</math> and <math>AC</math> at points <math>M</math> and <math>N</math> res...")
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Problem

The circumference inscribed in triangle $ABC$, is tangent to sides $AB$ and $AC$ at points $M$ and $N$ respectively. The bisectors of $A$ and $B$ intersect $MN$ at points $P$ and $Q$ respectively. Let $O$ be the incenter of triangle $ABC$. Prove: \[(MP)(OA)=(BC)(OQ)\]

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

Solution

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