2013 OIM Problems/Problem 4

Problem

Let $\Gamma$ be a circle with center $O$, $AE$ be a diameter of $\Gamma$ and $B$ be the midpoint of one of the arcs $AE$ of $\Gamma$. Point $D \ne E$ is on segment $OE$. Point $C$ is such that the quadrilateral $ABCD$ is a parallelogram with $AB$ parallel to $CD$ and $BC$ parallel to $AD$. The lines $EB$ and $CD$ intersect at point $F$. The line $OF$ cuts the minor arc $EB$ of $\Gamma$ at point $I$. Prove that the line $EI$ is the bisector of the angle $BEC$.

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

Solution

This problem needs a solution. If you have a solution for it, please help us out by adding it.

See also

OIM Problems and Solutions