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The nine-point circle of a triangle ABC is so named because it passes through nine special points:

1-3. midpoints of the sides of the triangle
4-6. feet of the altitudes
7-9. midpoints between the orthocenter, H, and the vertices A, B, and C. Triangle 123 is the medial triangle of triangle ABC. Triangle 456 is the orthic triangle of triangle ABC. Triangle 789 is the Euler triangle of triangle ABC. Which two stay similar to triangle ABC when you drag point B?

For more, see GEOMETRY IN ACTION, Chapter 2.