Christopher J. Bradley and Geoff C. Smith, The locations
of triangle centers,
Forum Geometricorum, 6 (2006) 57--70.
Abstract: The orthocentroidal circle of
a non-equilateral triangle has diameter GH where G is the centroid and H
is the orthocenter. We show that the Fermat, Gergonne and symmedian points
are confined to, and range freely over the interior disk punctured at its
center. The Mittenpunkt is also confined to and ranges freely over another
punctured disk, and the second Fermat point is confined to and ranges freely
over the exterior of the orthocentroidal circle. We also show that the circumcenter,
centroid and symmedian point determine the sides of the reference triangle
ABC.
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