symmedian

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

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.

Title	symmedian
Canonical name	Symmedian
Date of creation	2013-03-22 12:10:55
Last modified on	2013-03-22 12:10:55
Owner	drini (3)
Last modified by	drini (3)
Numerical id	6
Author	drini (3)
Entry type	Definition
Classification	msc 51M99
Related topic	Triangle
Related topic	LemoinePoint
Related topic	GergonnePoint
Related topic	Isogonal
Related topic	IsogonalConjugate
Related topic	FundamentalTheoremOnIsogonalLines
Related topic	LemoineCircle