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Feuerbach's Theorem

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The nine-point circle of a triangle passes through the feet of the altitudes, the midpoints of the sides, and the midpoints between the vertices and the orthocenter.

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The nine-point circle is internally tangent to the incircle and externally tangent to the three excircles.

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Contributed by: Jay Warendorff (March 2011)
Open content licensed under CC BY-NC-SA

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