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find an angle, related to 3 equal collinear segments + 3 equilateral triangles

Source: Peru MO 2005 level 3 p3

May 16, 2019
geometryangleEquilateral TriangleEquilateralequal segments

Problem Statement

Let A,B,C,DA,B,C,D, be four different points on a line ℓ\ell, so that AB=BC=CDAB=BC=CD. In one of the semiplanes determined by the line ℓ\ell, the points PP and QQ are chosen in such a way that the triangle CPQCPQ is equilateral with its vertices named clockwise. Let MM and NN be two points of the plane be such that the triangles MAPMAP and NQDNQD are equilateral (the vertices are also named clockwise). Find the angle ∠MBN\angle MBN.
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