Nine point circle

Triangle ABC with the nine point circle in light orange

The nine point circle (also known as Euler's circle or Feuerbach's circle) of a given triangle is a circle which passes through 9 "significant" points:

• The three feet of the altitudes of the triangle.
• The three midpoints of the edges of the triangle.
• The three midpoints of the segments joining the vertices of the triangle to its orthocenter. (These points are sometimes known as the Euler points of the triangle.)

That such a circle exists is a non-trivial theorem of Euclidean geometry.

The center of the nine point circle is the nine-point center and is usually denoted .

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