Paul Yiu, On the Fermat lines,
Forum Geometricorum 3 (2003) 73--81.

Abstract:  We study the triangle formed by three points each  on a Fermat line of a given triangle, and at equal distances from the vertices.  For two specific values of the common distance, the triangle degenerates  into a line. The two resulting lines are the axes of the Steiner ellipse of the triangle.

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