Toufik Mansour and Mark Shattuck, Some monotonicity results related to the Fermat point of a triangle,
Forum Geometricorum, 16 (2016) 355--366.

Abstract. In this paper, we establish a Fermat point analogue of the Steiner-Lehmus theorem by proving a more general monotonicity property. We also consider four pairs of segment lengths determined by intersecting Fermat point cevians to unequal sides of a triangle and determine comparable properties for these segments. Our proofs make use of trigonometric inequalities.

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