Journal for Geometry and Graphics 12 (2008), No. 1, 075--080
Copyright Heldermann Verlag 2008
Conic Solution of Euler's Triangle Determination Problem
Dept. of Mathematical Sciences, Florida Atlantic University, Boca Raton, FL 33431, U.S.A.
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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