2019 IMO Problems/Problem 6

Revision as of 22:31, 26 May 2020 by Ultraman (talk | contribs) (Problem)


Let $I$ be the incenter of acute triangle $ABC$ with $AB \neq AC$. The incircle ω of $ABC$ is tangent to sides $BC$, $CA$, and $AB$ at $D$, $E$, and $F$, respectively. The line through $D$ perpendicular to $EF$ meets ω again at $R$. Line $AR$ meets ω again at P. The circumcircles of triangles PCE and PBF meet again at Q. Prove that lines $DI$ and $PQ$ meet on the line through $A$ perpendicular to $AI$.

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