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NinePointCircle

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.