![cover image](https://wikiwandv2-19431.kxcdn.com/_next/image?url=https://upload.wikimedia.org/wikipedia/commons/thumb/5/5f/Triangle.NinePointCircle.svg/640px-Triangle.NinePointCircle.svg.png&w=640&q=50)
Nine-point circle
Circle constructed from a triangle / From Wikipedia, the free encyclopedia
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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).[1][2]
![Thumb image](http://upload.wikimedia.org/wikipedia/commons/thumb/5/5f/Triangle.NinePointCircle.svg/200px-Triangle.NinePointCircle.svg.png)
![Thumb image](http://upload.wikimedia.org/wikipedia/commons/thumb/7/7a/EulerCircle4.gif/320px-EulerCircle4.gif)
Triangle sides
Note that the construction still works even if the orthocenter and circumcenter fall outside of the triangle.The nine-point circle is also known as Feuerbach's circle (after Karl Wilhelm Feuerbach), Euler's circle (after Leonhard Euler), Terquem's circle (after Olry Terquem), the six-points circle, the twelve-points circle, the n-point circle, the medioscribed circle, the mid circle or the circum-midcircle. Its center is the nine-point center of the triangle.[3][4]