Τρίτη, 17 Οκτωβρίου 2017

2002 IMO Shortlist G3

The circle $S$ has centre $O$, and $BC$ is a diameter of $S$. Let $A$ be a point of $S$ such that $\angle AOB < 120^\circ$. Let $D$ be the midpoint of the arc $AB$ which does not contain $C$. The line  through $O$ parallel to $DA$ meets the line $AC$ at I. The perpendicular bisector of $OA$ meets $S$ at $E$ and at $F$. Prove that $I$ is the incentre of the triangle $CEF$.

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