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fundamental theorem on isogonal lines (Theorem)

Let $\triangle ABC$ be a triangle and $AX, BY, CZ$ three concurrent lines at $P$. If $AX',BY', CZ'$ are the respective isogonal conjugate lines for $AX,BY,CZ$, then $AX', BY',CZ'$ are also concurrent at some point $P'$.

An applications of this theorem proves the existence of Lemoine point (for it is the intersection point of the symmedians):

\includegraphics{lemoinep}

This theorem is a direct consequence of Ceva's theorem (trigonometric version).



"fundamental theorem on isogonal lines" is owned by drini. [ owner history (1) ]
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See Also: isogonal, isogonal conjugate, Lemoine point, symmedian, triangle
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Cross-references: Ceva's theorem, consequence, symmedians, intersection, Lemoine point, theorem, applications, point, isogonal conjugate, lines, concurrent, triangle
There is 1 reference to this entry.

This is version 1 of fundamental theorem on isogonal lines, born on 2002-09-02.
Object id is 3407, canonical name is FundamentalTheoremOnIsogonalLines.
Accessed 2519 times total.

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AMS MSC: 51-00 (Geometry :: General reference works )
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