Forum Geometricorum, 2 (2002) 93--104.

Abstract: Given three points O, G, I, we give a
simple construction by paper-folding for a triangle having these points
as circumcenter, centroid, and incenter. If two further points H and N
are defined by **OH** = 3**OG** = 2**ON**, we prove that this
procedure is successful if and only if I lies inside the circle on GH as
diameter and differs from N. This locus for I is also independently derived
from a famous paper of Euler, by complementing his calculations and properly
discussing the reality of the roots of an algebraic equation of degree
3.

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