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Orthocenter of A Triangle. Definition of the Orthocenter of a Triangle: The orthocenter is one of the triangle's points of concurrency formed by the intersection of the triangle 's 3 altitudes.
Denote the vertices of a triangle as A, B, and C and the orthocenter as H, and let D, E, and F denote the feet of the altitudes from A, B, and C respectively. Then: The sum of the ratios on the three altitudes of the distance of the orthocenter from the base to the length of the altitude is 1: