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ABM, BCN and CAP are similar

Source: Romanian MO 2010 Grade 10

August 6, 2012
searchgeometrysimilar trianglesgeometry proposed

Problem Statement

On the exterior of a non-equilateral triangle ABCABC consider the similar triangles ABM,BCNABM,BCN and CAPCAP, such that the triangle MNPMNP is equilateral. Find the angles of the triangles ABM,BCNABM,BCN and CAPCAP.
Nicolae Bourbacut