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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Nine Point Circle
First, draw the midpoint of each side of the triangle. Next, draw the projection of each vertex onto the opposite side of the triangle. And finally, find the midpoint of each vertex with the orthocenter of the triangle.

Amazingly, these nine points all lie on the same circle. Pick any three of these points and draw a circle through them. As you will see, the other six points you didn't select are also on this circle.