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 Circle: Significant Nine Points, Discovery, Tangent Circles, Other Properties of The Nine-point Circle

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**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 ...### Famous quotes containing the word circle:

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