### The Nine Point Circle

by
#### Julia Neal

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.

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