We group triangles into families based on three parameters: the distance between the circumcenter O and the centroid G, the circumradius, and the measure of angle Ð GOAwhere A is one vertex. We focus on the family of triangles which allows Ð GOA to vary and fixes the other two parameters. By construction, this grouping produces triangles which share the same Euler line. Perhaps unexpectedly, if we examine the family's locus of a triangle center known as the symmedian point, we find that it always forms an arc of a circle centered at a specified point on the Euler line.
Steve Kennedy, Department of Mathematics, Carleton Collegeskennedy@carleton.edu
Carr, Adam; Fisher, Julia; Roberts, Andrew; and Xu, Peng (David)
"Natural Families of Triangles II: A Locus of Symmedian Points,"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 9
, Article 3.
Available at: http://scholar.rose-hulman.edu/rhumj/vol9/iss1/3