O. R. Kayumov, K. E. Kashirina, “Elementary proof of Steinharz hypothesis”, Math. Ed., 2015, Issue 3(75),Pages <nobr>2

Students and teachers of secondary school

Elementary proof of Steinharz hypothesis

O. R. Kayumov, K. E. Kashirina

Omsk State Pedagogical University, branch in the town of Tara

Abstract: Let a triangle be divided in six smaller triangles by bisectors. The Steinharz hypothesis claims that the centers of the incircles of these six triangles belong to an ellipsis. The authors suggest an elementary proof.

Keywords: subdivision of a triangle by its bysectors, centers of the incircles of the subdivision triangles, the common ellipsis of the centers.

UDC: 514.112.3