Euler line
In any triangle 
, the Euler line is a line which passes through the orthocenter 
, centroid 
, circumcenter 
, nine-point center 
and De Longchamps point 
. It is named after Leonhard Euler. Its existence is a non-trivial theorem of Euclidean geometry.
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Certain fixed orders and distance ratios hold among these points. In particular, 
and 
Given the orthic triangle
of , the Euler lines of 
,
, and 
concur at , the nine-point center of .
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