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.
yiu@fau.edu
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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