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The Nine-point Circle

Author:Irina Boyadzhiev
Given is any triangle ABC. (Drag points A, B or C to change it).
  • MAB, MBC and MAD (in red) are the midpoints of the sides of the triangle .
  • HA, HB and HC(in green) are the feet of the altitudes of the triangle.
  • K, L and M (in orange) are the midpoints of the three segments from the orthocenter to the vertices.
Theorem: All of these nine points lie on the same circle - the nine-point circle or also Euler's circle. In GeoGebra: If we construct a circle through any three of these points, the other six will lie on the same circle. Use the relation tool to confirm this.

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