A Theorem about Simultaneous Orthological and Homological Triangles

Ion Patrascu; Florentin Smarandache

paper

A Theorem about Simultaneous Orthological and Homological Triangles

arXiv:1004.0347

Abstract

In this paper we prove that if $P_{1}, P_{2}$ are isogonal points in the triangle $A B C$ , and if $A_{1} B_{1} C_{1}$ and $A_{2} B_{2} C_{2}$ are their corresponding pedal triangles such that the triangles $A B C$ and $A_{1} B_{1} C_{1}$ are homological (the lines $A A_{1}, B B_{1}, C C_{1}$ are concurrent), then the triangles $A B C$ and $A_{2} B_{2} C_{2}$ are also homological.

13 pages, 10 geometrical figures