
Journal for Geometry and Graphics 19 (2015), No. 2, 211218 Copyright Heldermann Verlag 2015 Cevian Cousins of a Triangle Centroid Bojan Hvala FNM, University of Maribor, Koroska cesta 160, 2000 Maribor, Slovenia bojan.hvala@um.si According to Seebach's theorem there exist six points inside a triangle with Cevian triangles similar to the reference triangle. Besides the centroid, other five points M, M', M_{A}, M_{B}, M_{C} are generally not constructable with ruler and compass. We present an access to these five points using an additional tool: a possibility to draw a conic through five given points. We provide information on barycentric coordinates of these five points and prove that M_{A}M_{B}M_{C} is a central triangle of type 2 and that points M and M' are Brocardians of each other. Keywords: Cevian triangle, Seebach's theorem, constructability with ruler and compass, conics, central triangle, Brocardian. MSC: 51M15; 51N20, 51M04 [ Fulltextpdf (167 KB)] 