The Euler points are the midpoints 
, 
,
of the segments which join the vertices 
, 
,
and 
of a triangle 
and the orthocenter 
. They are three of the nine prominent
points of a triangle through which the nine-point
circle passes. The Euler points determine the Euler
triangle 
.
Given a triangle 
,
construct the orthic triangle 
. Then the Euler lines
of the three corner triangles 
, 
and 
pass through the Euler points, and concur at a
point 
on the nine-point circle of triangle 
such that one of
 |  |  |
(1)
|
 |  |  |
(2)
|
 |  |  |
(3)
|
holds (Thébault 1947, 1949; Thébault et al. 1951).
