Geodesic
Conic Construction of a Triangle from the Feet of Its Angle Bisectors
Journal for geometry and graphics, Tome 12 (2008) no. 2, pp. 171-182 Cet article a éte moissonné depuis la source Heldermann Verlag

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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.
Classification : 51M05, 51M15
Mots-clés : Angle bisector problem, anticevian triangle, conics, cubics, isogonal conjugates, harmonic conjugates 
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     author = {P. Yiu },
     title = {Conic {Construction} of a {Triangle} from the {Feet} of {Its} {Angle} {Bisectors}},
     journal = {Journal for geometry and graphics},
     pages = {171--182},
     year = {2008},
     volume = {12},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/JGG_2008_12_2_JGG_2008_12_2_a5/}
}
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P. Yiu . Conic Construction of a Triangle from the Feet of Its Angle Bisectors. Journal for geometry and graphics, Tome 12 (2008) no. 2, pp. 171-182. http://geodesic.mathdoc.fr/item/JGG_2008_12_2_JGG_2008_12_2_a5/