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 points, six lying on the triangle itself. They include

Related Topics:
Geometry - Circle - Triangle

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• the midpoints of the three sides of the triangle,
• the feet of the triangle's altitudes,
• the points on each altitude of the triangle that bisect the line from the altitude's vertex to the triangle's orthocenter.

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.

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Nine point circle: Significant points ►