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.
