A Theorem about Simultaneous Orthological and Homological Triangles

Details A Theorem about Simultaneous Orthological and Homological Triangles A Theorem about Simultaneous Orthological and Homological Triangles

2010-04-02

arxiv.org/abs/1004.0347v1

Mathematics

General Mathematics

13 pages, 10 geometrical figures

Scientific paper

In this paper we prove that if $P_1, P_2$ are isogonal points in the triangle
$ABC$, and if $A_1B_1C_1$ and $A_2B_2C_2$ are their corresponding pedal
triangles such that the triangles $ABC$ and $A_1B_1C_1$ are homological (the
lines $AA_1, BB_1, CC_1$ are concurrent), then the triangles $ABC$ and
$A_2B_2C_2$ are also homological.

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