The Common Nine-point Circle
The center of this common nine-point circle lies at the centroid of the four orthocentric points. The radius of the common nine-point circle is the distance from the nine-point center to the midpoint of any of the six connectors that join any pair of orthocentric points through which the common nine-point circle passes. The nine-point circle also passes through the three orthogonal intersections at the feet of the altitudes of the four possible triangle.
This common nine-point center lies at the midpoint of the connector that joins any orthocentric point to the circumcenter of the triangle formed from the other three orthocentric points.
Read more about this topic: Orthocentric System
Famous quotes containing the words common and/or circle:
“It is common knowledge to every schoolboy and even every Bachelor of Arts,
That all sin is divided into two parts.
One kind of sin is called a sin of commission, and that is very
important,”
—Ogden Nash (1902–1971)
“A circle swoop, and a quick parabola under the bridge arches
Where light pushes through;
A sudden turning upon itself of a thing in the air.
A dip to the water.”
—D.H. (David Herbert)