what is nine point circle

The nine-point circle, also called Euler's circle or the Feuerbach circle, is the circle that passes through the perpendicular feet H_A, H_B, and H_C dropped from the vertices of any refrence triangle DeltaABC on the sides opposite them. Euler showed in 1765 that it also passes through the midpoints M_A, M_B, M_C of the sides of DeltaABC. ByFeuerbach's theorem , the nine-point circle also passes through the midpoints E_A, E_B, and E_C of the segments that join the vertices and the orthocenter H. These points are commonly referred to as the Euler points. These three triples of points make nine in all, giving the circle its name. The nine-point circle is the complement of the circumcircle. The nine-point circle has circle function

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