Joseph Stern, Euler's triangle determination problem,
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.