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Journal for Geometry and Graphics 19 (2015), No. 2, 211--218
Copyright Heldermann Verlag 2015

Cevian Cousins of a Triangle Centroid

Bojan Hvala
FNM, University of Maribor, Koroska cesta 160, 2000 Maribor, Slovenia

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', MA, MB, MC 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 MAMBMC 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

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