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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