Nine-point Circle

In geometry, the nine-point circle is a circle that can be constructed for any given triangle. It is so named because it passes through nine significant concyclic points defined from the triangle. These nine points are:

  • The midpoint of each side of the triangle
  • The foot of each altitude
  • The midpoint of the line segment from each vertex of the triangle to the orthocenter (where the three altitudes meet; these line segments lie on their respective altitudes).

The nine-point circle is also known as Feuerbach's circle, Euler's circle, Terquem's circle, the six-points circle, the twelve-points circle, the n-point circle, the medioscribed circle, the mid circle or the circum-midcircle.

Read more about Nine-point CircleSignificant Nine Points, Discovery, Tangent Circles, Other Properties of The Nine-point Circle

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circle" class="article_title_2">Other Properties of The Nine-point Circle
... The radius of a triangle's circumcircle is twice the radius of that triangle's nine-point circle ... Figure 3 A nine-point circle bisects a line segment going from the corresponding triangle's orthocenter to any point on its circumcircle ... Figure 4 The center of any nine-point circle (the nine-point center) lies on the corresponding triangle's Euler line, at the midpoint between that ...

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