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Nine-Point Center

The center $F$ (or $N$) of the Nine-Point Circle. It has Triangle Center Function

$\displaystyle \alpha$ $\textstyle =$ $\displaystyle \cos(B-C)=\cos A+2\cos B\cos C$  
  $\textstyle =$ $\displaystyle bc[a^2b^2+a^2c^2+(b^2-c^2)^2],$  

and is the Midpoint of the line between the Circumcenter $C$ and Orthocenter $H$. It lies on the Euler Line.

See also Euler Line, Nine-Point Circle, Nine-Point Conic


Carr, G. S. Formulas and Theorems in Pure Mathematics, 2nd ed. New York: Chelsea, p. 624, 1970.

Dixon, R. Mathographics. New York: Dover, pp. 57-58, 1991.

Kimberling, C. ``Central Points and Central Lines in the Plane of a Triangle.'' Math. Mag. 67, 163-187, 1994.

Kimberling, C. ``Nine-Point Center.''

© 1996-9 Eric W. Weisstein