Lemoine point
The Lemoine point of a triangle
, is the intersection
point of its three symmedians
. (That is, the isogonal conjugate
of the centroid).
It is related with the Gergonne point by the following result:
On any triangle , the Lemoine point of its Gergonne triangle is the Gergonne point of .
In the picture, the blue lines are the medians, intersecting an the centroid .
The green lines are anglee bisectors intersecting at the incentre and the red lines are symmedians. The symmedians intersect at Lemoine point .
| Title | Lemoine point |
| Canonical name | LemoinePoint |
| Date of creation | 2013-03-22 12:11:02 |
| Last modified on | 2013-03-22 12:11:02 |
| Owner | drini (3) |
| Last modified by | drini (3) |
| Numerical id | 9 |
| Author | drini (3) |
| Entry type | Definition |
| Classification | msc 51-00 |
| Related topic | Triangle |
| Related topic | Symmedian |
| Related topic | LemoineCircle |
| Related topic | Incircle |
| Related topic | Centroid |
| Related topic | Incenter |
| Related topic | GergonnePoint |
| Related topic | Isogonal |
| Related topic | IsogonalConjugate |
| Related topic | FundamentalTheoremOnIsogonalLines |