WOLFRAM|DEMONSTRATIONS PROJECT

The Center and Radius of the Nine-Point Circle

​
circumcircle radii
nine-point circle radii
R
≈
0.92
r
≈
0.46
2
×
r
≈
0.92
ON
≈
0.25
NH
≈
0.25
Let ABC be a triangle with orthocenter H, circumcenter O, and circumradius
R
. Let the nine-point circle have center N and radius
r
.
Then N lies on OH (the Euler line) and bisects OH.
Also,
R=2r
.