2007 OIM Problems/Problem 2
Problem
Let be a triangle with incenter and be a circle with center , of radius greater than that of the inscribed circle and that does not pass through any of the vertices. Let be the point of intersection of with the line closest to ; , the points of intersection of with the line being closest to ; and the point of intersection of with the line closest to . Let be the point of intersection of the lines and . Show that intersects segment at its midpoint.
~translated into English by Tomas Diaz. ~orders@tomasdiaz.com
Solution
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