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

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Six Point Circle
Construct the centroid of the triangle below in the usual manner. That is, draw a line from each vertex to the midpoint of the opposite side. The intersection of these three lines is the centroid.

Notice that the centroid is always inside the triangle, and thus the three lines drawn divide the triangle into six smaller non-overlapping triangles. Find the circumcenters of each of these smaller triangles.

Amazingly, these six circumcenters all lie on the same circle. Draw a circle through any three of these points and see that the other three points also lie on this circle.