### What are the Circumcenter and the
Circumcircle?

by
### Julia Neal

The **Circumcenter** is the point of concurrency
of the perpendicular bisectors of the sides of a triangle.

The **circumcircle** is the circle whose
center is the circumcenter and whose radius is the length from
the circumcenter to any of the three vertices of the triangle.

Let's find the Circumcircle to the medial triangle.

Now let's look at the circumcircle to the orthic
triangle.

And last, let's look at the circumcircle to
the triangle formed by the midpoints to the segments from the
vertices of our original triangle to the orthocenter.

When we construct all three triangles with
their circumcenters and circumcircles, we can see that the circumcircles
are in fact one circle that contains the vertices of all three
triangles.

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