# Symmedians

Just as a side bisector of a triangle is also called the median, the mirror image of a side bisector at the corresponding angle bisector (i.e. at the angle bisector that starts from the same corner as the side bisector) is called a **symmetrian** . The term is an abbreviation for "symmetrical median", comes from the Greek and means "reflection on the center line".

The three symmedians of a triangle intersect at a point, the so-called *Lemoine point* ( *Lemoine point* ), which is also called *Grebe **point* or *symmetrian **point* . This can be proven with the help of Ceva's theorem.

The intersection of the symmedians is a non-canonical distinguished point of the triangle .

## literature

- Roger A. Johnson:
*Advanced Euclidean Geometry*. Dover 2007, ISBN 978-0-486-46237-0 , pp. 213, 268, 271, 303 (first published in 1929 by the Houghton Mifflin Company (Boston) under the title*Modern Geometry*).