
Journal for Geometry and Graphics 12 (2008), No. 2, 171182 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 rulerandcompass 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 [ Fulltextpdf (504 KB)] for subscribers only. 