David Little
Mathematics Department
Penn State University
Eberly College of Science
University Park, PA 16802
Office: 403 McAllister
Phone: (814) 865-3329
Fax: (814) 865-3735
e-mail:dlittle@psu.edu

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Euler's Line
The centroid (red), orthocenter (blue), circumcenter (green) and incenter (yellow) are all drawn below. Notice that the centroid, orthocenter and circumcenter all lie on a straight line. This line is known as Euler's line. The distance from the orthocenter to the centroid is exactly twice the distance from the centroid to the circumcenter.
  • What kind of triangle is it when all four points lie on Euler's line?
  • When do all four points coincide?
  • When does Euler's line divide the triangle into two smaller triangles of equal area?