Triangle/Nine-point circle/Fact

< Triangle < Nine-point circle
Theorem about the Nine-point circle

Let a nondegenerate triangle in the Euclidean plane with vertices be given. Let be the circumcircle of the midpoints of the sides of the triangle. Then the following statements hold.

  1. The radius of is half of the radius of the circumcircle of .
  2. The line segements between the orthocenter and the vertices are cut in halves by .
  3. The feet of the altitudes of lie on .
Proof, Write another proof
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