PlanetMath (more info)
 Math for the people, by the people.
Encyclopedia | Requests | Forums | Docs | Wiki | Random | RSS  
Login
create new user
name:
pass:
forget your password?
Main Menu
sections
Encyclopædia
Papers
Books
Expositions

meta
Requests (203)
Orphanage
Unclass'd
Unproven (490)
Corrections (7)
Classification

talkback
Polls
Forums
Feedback
Bug Reports

downloads
Snapshots
PM Book

information
News
Docs
Wiki
ChangeLog
TODO List
Legalese
About
Owner confidence rating: High Entry average rating: No information on entry rating
Lemoine point (Definition)

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 $ABC$, the Lemoine point of its Gergonne triangle is the Gergonne point of $ABC$.

\includegraphics{lemoinep}
In the picture, the blue lines are the medians, intersecting an the centroid $G$. The green lines are anglee bisectors intersecting at the incentre $I$ and the red lines are symmedians. The symmedians intersect at Lemoine point $L$.



"Lemoine point" is owned by drini. [ owner history (1) ]
(view preamble)

View style:

See Also: triangle, symmedian, Lemoine circle, incircle, centroid, incenter, Gergonne point, isogonal, isogonal conjugate, fundamental theorem on isogonal lines
Log in to rate this entry.
(view current ratings)

Cross-references: incentre, bisectors, medians, lines, Gergonne triangle, Gergonne point, centroid, isogonal conjugate, symmedians, point, intersection, triangle
There are 5 references to this entry.

This is version 5 of Lemoine point, born on 2002-01-08, modified 2002-05-17.
Object id is 1448, canonical name is LemoinePoint.
Accessed 3906 times total.

Classification:
AMS MSC: 51-00 (Geometry :: General reference works )
Pending Errata and Addenda
None.
Discussion
Style: Expand: Order:
forum policy

No messages.

Interact
post | correct | update request | add derivation | add example | add (any)