Problem 58956. Find the nine-point circle of a triangle
Cody Problem 1336 asks us to find the circle that circumscribes a triangle, and Cody Problem 58354 asks us to find the circle that is inscribed in a triangle. This problem deals with the nine-point circle of a triangle—the circle that passes through the midpoints of the sides, the feet of the altitudes, and the midpoints of the line segments connecting the vertices to the orthocenter (the intersection of the altitudes).
Write a function that takes the x- and y-coordinates of three points describing the vertices of a triangle and returns the center and radius of the nine-point circle, as well as the x- and y-coordinates of the nine points.
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