### 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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