IMO 2019/P6

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tanmoy
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IMO 2019/P6

Unread post by tanmoy » Thu Jul 18, 2019 11:13 pm

Let $I$ be the incentre of acute triangle $ABC$ with $AB\neq AC$. The incircle $\omega$ of $ABC$ is tangent to sides $BC$, $CA$, and $AB$ at $D$, $E$, and $F$, respectively. The line through $D$ perpendicular to $EF$ meets $\omega$ at $R$. Line $AR$ meets $\omega$ again at $P$. The circumcircles of triangle $PCE$ and $PBF$ meet again at $Q$.

Prove that lines $DI$ and $PQ$ meet on the line through $A$ perpendicular to $AI$.

Proposed by Anant Mudgal, India
"Questions we can't answer are far better than answers we can't question"

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