fundamental theorem on isogonal lines
Let be a triangle and three concurrent lines at .
If are the respective isogonal conjugate
lines for , then are also concurrent
at some point .
An applications of this theorem proves the existence of Lemoine point (for it is the intersection point of the symmedians
):
This theorem is a direct consequence of Ceva’s theorem (trigonometric version).
Title | fundamental theorem on isogonal lines |
---|---|
Canonical name | FundamentalTheoremOnIsogonalLines |
Date of creation | 2013-03-22 13:01:16 |
Last modified on | 2013-03-22 13:01:16 |
Owner | drini (3) |
Last modified by | drini (3) |
Numerical id | 4 |
Author | drini (3) |
Entry type | Theorem |
Classification | msc 51-00 |
Related topic | Isogonal |
Related topic | IsogonalConjugate |
Related topic | LemoinePoint |
Related topic | Symmedian |
Related topic | Triangle |