Nine-Point Circle
The Nine-Point circle for any triangle passes through the three mid-points of the sides, the three feet of the altitudes, and the three mid-points of the segments from thr respective vertices to orthocenter.

The center of the circle is labeled with an N.

 


Click here for a GSP script to consruct the nine-point circle of a triangle, given any three points (the vertcies of a triangle).

Click here for a GSP script to consruct the center of a nine-point circle of a triangle, given any three points (the vertcies of a triangle).

 Triangle Circles

Triangles

GSP Sketches

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