Sabrina Bier, Equilateral Triangles Intercepted by Oriented Parallelians

Forum Geometricorum, 1 (2001) 25 -- 32.

Abstract:   Given a point P in the plane of triangle ABC, we consider rays through P parallel to the side lines. The intercepts on the sidelines form an equilateral triangle precisely when P is a  Brocardian point of one of the Fermat points. There are exactly four such equilateral triangles.

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