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# Euler Points

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).

Euler Triangle, Feuerbach's Theorem, Nine-Point Circle, Orthic Triangle

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## References

Honsberger, R. Episodes in Nineteenth and Twentieth Century Euclidean Geometry. Washington, DC: Math. Assoc. Amer., p. 6, 1995.Thébault, V. "Concerning the Euler Line of a Triangle." Amer. Math. Monthly 54, 447-453, 1947.Thébault, V. "Problem 4328." Amer. Math. Monthly 56, 39-40, 1949.Thébault, V.; Ramler, O. J.; and Goormaghtigh, R. "Solution to Problem 4328: Euler Lines." Amer. Math. Monthly 58, 45, 1951.

Euler Points

## Cite this as:

Weisstein, Eric W. "Euler Points." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/EulerPoints.html