Forum Geometricorum, 7 (2007) 1--9.

Abstract: We give a simple proof of Euler's remarkable theorem that for a nondegenerate triangle, the set of points eligible to be the incenter is precisely the orthocentroidal disc, punctured at the nine-point center. The problem is handled algebraically with complex coordinates. In particular, we show how the vertices of the triangle may be determined from the roots of a complex cubic whose coefficients depend only on the classical centers.

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