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Concurrency from exterior equilateral triangles

Source: Baltic Way 2003

November 7, 2010
geometrygeometric transformationreflectionparallelogramtrapezoidgeometry unsolved

Problem Statement

Equilateral triangles AMB,BNC,CKAAMB,BNC,CKA are constructed on the exterior of a triangle ABCABC. The perpendiculars from the midpoints of MN,NK,KMMN, NK, KM to the respective lines CA,AB,BCCA, AB, BC are constructed. Prove that these three perpendiculars pass through a single point.
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