Problem

Source: Romanian I TST 2007

Tags: function, geometry, geometric transformation, reflection, geometry proposed



Let O1 and O2 two exterior circles. Let A, B, C be points on O1 and D, E, F points on O1 such that AD and BE are the common exterior tangents to these two circles and CF is one of the interior tangents to these two circles, and such that C, F are in the interior of the quadrilateral ABED. If CO1AB={M} and FO2DE={N} then prove that MN passes through the middle of CF.