Given is any triangle ABC. (Drag points A, B or C to change it).[br][list][br][*]MAB, MBC and MAD (in red) are the midpoints of the sides of the triangle .[br][*]HA, HB and HC(in green) are the feet of the altitudes of the triangle.[br][*] K, L and M (in orange) are the midpoints of the three segments from the orthocenter to the vertices. [br][/list][br][b][i]Theorem:[/i][/b] All of these nine points lie on the same circle - the nine-point circle or also Euler's circle.[br] 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.