The nine point circle is a circle that is created with 9 special points on it. These 9 points are the vertices of three special triangles.
The first triangle is the MEDIAL TRIANGLE. This triangle is formed by connectiong the midpoints of the three sides of a triangle.
The second triangle is the ORTHIC TRIANGLE. The orthic triangle is formed by connecting the feet of the three altitudes of the three sides of an original triangle.
The third triangle is created by finding the ORTHOCENTER of our original triangle. The midponts of the segments whose endpoints are the orthocenter and the vertices of the original triangle form the vertices of this triangle.
The actual circle is created by finding the CIRCUMCENTER of any of these three triangles. The circumcenters of these triangles is actually the same point. The circumcenter is the center of the nine point circle. The radius of the circle is the length to any of the nine points from the circumcenter. The nine point circle is the CIRCUMCIRCLE to each of these three triangles.
