MathDB
Bulgaria 4

Source: BMO Problem 4

May 15, 2005
geometrygeometric transformationrotationtrigonometrysimilar trianglesgeometry proposed

Problem Statement

Let ABCABC be a triangle with AC≠BCAC\neq BC, and let A′B′CA^{\prime }B^{\prime }C be a triangle obtained from ABCABC after some rotation centered at CC. Let M,E,FM,E,F be the midpoints of the segments BA′,ACBA^{\prime },AC and CB′CB^{\prime } respectively. If EM=FMEM=FM, find EMF^\widehat{EMF}.
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