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<MBN=? AB=BC=CD, equilaterals MAP, NQD 2016 Ecuador NMO (OMEC) 3.3

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September 17, 2021
anglesequilateralsequal segmentsgeometry

Problem Statement

Let A,B,C,DA, B, C, D be four different points on a line ℓ\ell, such 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 on the plane such that the triangles MAPMAP and NQDNQD are equilateral (the vertices are also named clockwise). Find the measure of the angle ∠MBN\angle MBN.
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