First triangle ABC was constructed. Then I constructed the orthocenter
of ABC. I connected the orthocenter (H) with vertex B, vertex C, and vertex
A. Once this was done, I constructed the orthocenters of triangles HAB,
HAC, and HBC.
Things discovered:
- The orthocenter of triangle ABC is H.
- The orthocenter of triangle HBC is A.
- The orthocenter of triangle HAB is C.
- The orthocenter of triangle HAC is B.
So the triangles formed with two vertices and the orthocenter of the original
triangle has an orthocenter that corresponds with the other vertex.
Next I constructed the nine-point circle of each of the four triangles.
What do you expect happened? It turns out that all three nine-point circles
of three new triangles correspond to the nine-point circle of the original
triangle ABC. The following is a construction of all four nine-point circles:
