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exists points such that BNC and DNA are equilateral, <AMB=<CMD=120^o

Source: Tournament of Towns Spring 1998 Seniors A p4

May 11, 2020
Equilateralgeometryisosceles

Problem Statement

A point MM is found inside a convex quadrilateral ABCDABCD such that triangles AMBAMB and CMDCMD are isoceles (AM=MB,CM=MDAM = MB, CM = MD) and ∠AMB=∠CMD=120o\angle AMB= \angle CMD = 120^o . Prove that there exists a point N such that trianglesBNC BNC and DNADNA are equilateral.
(I.Sharygin)
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