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The Circumcircles of triangles AHC, CHB, and BHA intersect at the orthocenter of triangle ABC.

The circumcircle of a triangle is a circle which is circumscribed on triangle ABC. This means that the circle passes through each of the vertices of the triangle. If H is the orthocenter of triangle ABC and H is also a point on each of the smaller triangles being considered, then by the definition of circumcircle, each of these circumcircles must pass through the point H.