2002 IMO Problems/Problem 2

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Problem

$\text{BC is a diameter of a circle center O. A is any point on the circle with } \angle AOC \not\le 60$
$\text{ EF is the chord which is the perpendicular bisector of AO. D is the midpoint of the minor arc AB. The line through
$ (Error compiling LaTeX. Unknown error_msg)\text{O parallel to AD meets AC at J. Show that J is the incenter of triangle CEF.}$