Nine-point Circle - Significant Nine Points

Significant Nine Points

The diagram above shows the nine significant points of the nine-point circle. Points D, E, and F are the midpoints of the three sides of the triangle. Points G, H, and I are the feet of the altitudes of the triangle. Points J, K, and L are the midpoints of the line segments between each altitude's vertex intersection (points A, B, and C) and the triangle's orthocenter (point S).

For an acute triangle, six of the points (the midpoints and altitude feet) lie on the triangle itself; for an obtuse triangle two of the altitudes have feet outside the triangle, but these feet still belong to the nine-point circle.

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