Open AccessISOSCELES TRIANGLES ON THE SIDES OF A TRIANGLE
Author(s) -
Sead Rešić,
Alma Šehanović,
Amila Osmić
Publication year - 2019
Publication title -
human
Language(s) - English
Resource type - Journals
eISSN - 2232-996X
pISSN - 2232-9935
DOI - 10.21554/hrr.041915
Subject(s) - isosceles triangle , equilateral triangle , combinatorics , quadrilateral , mathematics , point (geometry) , fermat's last theorem , intersection (aeronautics) , geometry , physics , engineering , finite element method , thermodynamics , aerospace engineering
Famous construction of Fermat-Toricelly point of a triangle leads to the question is there a similar way to construct other isogonic centers of a triangle in a similar way. For a purpose we remember that Fermat-Torricelli point of a triangle ΔABC is obtained by constructing equilateral triangles outwardly on the sides AB,BC and CA. If we denote thirth vertices of those triangles by C1 ,A1 and B1 respectively, then the lines AA1 ,BB1 and CC1 concurr at the Fermat-Torricelli point of a triangle ΔABC (Van Lamoen, 2003). In this work we present the condition for the concurrence, of the lines AA1 ,BB1 and C1 , where C1 ,A1 and B1 are the vertices of an isosceles triangles constructed on the sides AB,BC and CA (not necessarily outwordly) of a triangle ΔABC. The angles at this work are strictly positive directed so we recommend the reader to pay attention to this fact.