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:
“Though there are wreck-masters appointed to look after valuable property which must be advertised, yet undoubtedly a great deal of value is secretly carried off. But are we not all wreckers contriving that some treasure may be washed up on our beach, that we may secure it, and do we not infer the habits of these Nauset and Barnegat wreckers, from the common modes of getting a living?”
—Henry David Thoreau (1817–1862)
“Change begets change. Nothing propagates so fast. If a man habituated to a narrow circle of cares and pleasures, out of which he seldom travels, step beyond it, though for never so brief a space, his departure from the monotonous scene on which he has been an actor of importance would seem to be the signal for instant confusion.... The mine which Time has slowly dug beneath familiar objects is sprung in an instant; and what was rock before, becomes but sand and dust.”
—Charles Dickens (1812–1870)