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The same angles

Source: China South East Mathematical Olympiad2011

August 18, 2011
geometrycircumcircleprojective geometrygeometry proposed

Problem Statement

Let OO be the circumcenter of triangle ABCABC , a line passes through OO intersects sides AB,ACAB,AC at points M,NM,N , EE is the midpoint of MCMC , FF is the midpoint of NBNB , prove that : ∠FOE=∠BAC\angle FOE= \angle BAC
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