Journal for Geometry and Graphics 12 (2008), No. 1, 075--080
Copyright Heldermann Verlag 2008
Conic Solution of Euler's Triangle Determination Problem
Paul Yiu
Dept. of Mathematical Sciences, Florida Atlantic University, Boca Raton, FL 33431, U.S.A.
yiu@fau.edu
We study Euler's problem of determination of a triangle from its circumcenter, orthocenter, and incenter as a problem of geometric construction. While it cannot be solved using ruler and compass, we construct the vertices by intersecting a circle with a rectangular hyperbola, both easily constructed from the given triangle centers.
Keywords: Circumcenter, orthocenter, incenter, Feuerbach point, rectangular hyperbola.
MSC: 51M04; 51M15
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