1997 OIM Problems/Problem 2
Problem
With the center at the incenter of a triangle , a circle is drawn that cuts each of the three sides of the triangle at two points: the segment at and ( being the closest to ); the the segment in and ( being the closest to ), and the segment in and ( being the closest to ). Let be the point of intersection of the diagonals of the quadrilateral . Let be the point of intersection of the diagonals of the quadrilateral. Let be the point of intersection of the diagonals of the quadrilateral . Show that the circles circumscribed by the triangles , and have a single common point.
~translated into English by Tomas Diaz. ~orders@tomasdiaz.com
Solution
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