Geodesic
Conic Construction of a Triangle From Its Incenter, Nine-point Center, and a Vertex
Journal for geometry and graphics, Tome 16 (2012) no. 2, pp. 171-183 Cet article a éte moissonné depuis la source Heldermann Verlag

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We construct a triangle given its incenter, nine-point center and a vertex by locating the circumcenter as an intersection of two rectangular hyperbolas. Some special configurations leading to solutions constructible with ruler and compass are studied. The related problem of construction of a triangle given its circumcenter, incenter, and one vertex is revisited, and it is established that such a triangle exists if and only if the incenter lies inside the cardioid relative to the circumcircle.
Classification : 51M15, 51M04
Mots-clés : Triangle geometry, construction problems, nine-point center, rectangular hyperbolas 
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     author = {P. Yiu },
     title = {Conic {Construction} of a {Triangle} {From} {Its} {Incenter,} {Nine-point} {Center,} and a {Vertex}},
     journal = {Journal for geometry and graphics},
     pages = {171--183},
     year = {2012},
     volume = {16},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/JGG_2012_16_2_JGG_2012_16_2_a4/}
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P. Yiu . Conic Construction of a Triangle From Its Incenter, Nine-point Center, and a Vertex. Journal for geometry and graphics, Tome 16 (2012) no. 2, pp. 171-183. http://geodesic.mathdoc.fr/item/JGG_2012_16_2_JGG_2012_16_2_a4/