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Journal for Geometry and Graphics 12 (2008), No. 2, 171--182
Copyright Heldermann Verlag 2008

Conic Construction of a Triangle from the Feet of Its Angle Bisectors

Paul Yiu
Dept. of Mathematical Sciences, Florida Atlantic University, Boca Raton, FL 33431, U.S.A.

We study an extension of the problem of construction of a triangle from the feet of its internal angle bisectors. Given a triangle $ABC$, we give a conic construction of points which are the incenter or excenters of their own anticevian triangles with respect to ABC. If the given triangle contains a right angle, a very simple ruler-and-compass construction is possible. We also examine the case when the feet of the three external angle bisectors are three given points on a line.

Keywords: Angle bisector problem, anticevian triangle, conics, cubics, isogonal conjugates, harmonic conjugates.

MSC: 51M05; 51M15

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