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symmedian (Definition)

On any triangle, the three lines obtained by reflecting the medians in the (internal) angle bisectors are called the symmedians of the triangle.

\includegraphics{symmed}
In the picture, $BX$ is angle bisector and $BM$ a median. The reflection of $BM$ on $BX$ is $BN$, a symmedian.

It can be stated as symmedians are isogonal conjugates of medians.



"symmedian" is owned by drini. [ owner history (1) ]
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See Also: triangle, Lemoine point, Gergonne point, isogonal, isogonal conjugate, fundamental theorem on isogonal lines, Lemoine circle
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Cross-references: isogonal conjugates, reflection, angle bisectors, medians, lines, triangle
There are 3 references to this entry.

This is version 2 of symmedian, born on 2002-01-08, modified 2002-05-16.
Object id is 1445, canonical name is Symmedian.
Accessed 2093 times total.

Classification:
AMS MSC: 51M99 (Geometry :: Real and complex geometry :: Miscellaneous)
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