Dixon J. Jones, The periambic constellation: Altitudes, perpendicular bisectors, and other radical axes in a triangle,
Forum Geometricorum, 17 (2017) 383--399.
Abstract. Six circles may be constructed using a triangle's vertices as
centers and its sides as radii. These circles determine twelve
ordinary and three ideal radical axes, whose intersection points
include the triangle's circumcenter and orthocenter, along with
eight other ordinary points in interesting configurations. For
instance, we show that the orthocenter, circumcenter, and two
radical centers of the six circles form a parallelogram, and that
six other radical centers (the intersection points of the
altitudes and perpendicular bisectors) are the vertices of two
congruent triangles which are inversely similar to the original.
Underlying this ``constellation" is a simple invariance property
of three circles in which two are concentric.
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