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?