The problem of characterizing automedian triangles was posed in the late 19th century in the Educational Times (in French) by Joseph Jean Baptiste Neuberg, and solved there with the formula 2a2 = b2 + c2 by W. J. Greenstreet.
The Neuberg cubic (named after Joseph Jean Baptiste Neuberg) is the locus of a point X such that X* is on the line EX, where E is the Euler infinity point (X(30) in the Encyclopedia of Triangle Centers).
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