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 fact of Euclidean geometry.
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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