Nine-point circle

Even if the orthocenter and circumcenter fall outside of the triangle, the construction still works.

The nine-point circle is tangent to the incircle and excircles

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 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. Its center is the nine-point center of the triangle.

单词	Nine points circle
释义	Nine points circle 英语百科 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 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. Its center is the nine-point center of the triangle.
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Nine points circle

Nine-point circle