Nine point circle


If L, M and P are the midpoints of sides the sides, D, E, and F are the three feet of the altitudes, and Q, R and S are the midpoints of the lines joining the vetrices to the orthocenter of the triangle. Then the nine points L, M, P, Q, R, S, D, E and F lie on a circle whose radius is one half the radius of the circumcircle and whose center (N) lies on the Euler Line and is the midpoint between the Circumcenter (C) and Orthocenter (H).

Proof of the existence of the nine point circle.

To play with a GSP sketch that shows the nine point circle click here.



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