In geometry, the nine-point circle is a circle that can be constructed for any given triangle. It is so named because it passes through nine significant concyclic points defined from the triangle. These nine points are:
- The midpoint of each side of the triangle
- The foot of each altitude
- The midpoint of the line segment from each vertex of the triangle to the orthocenter (where the three altitudes meet; these line segments lie on their respective altitudes).
The nine-point circle is also known as Feuerbach's circle, Euler's circle, Terquem's circle, the six-points circle, the twelve-points circle, the n-point circle, the medioscribed circle, the mid circle or the circum-midcircle.
Read more about Nine-point Circle: Significant Nine Points, Discovery, Tangent Circles, Other Properties of The Nine-point Circle
Famous quotes containing the word circle:
“It is a good lesson—though it may often be a hard one—for a man who has dreamed of literary fame, and of making for himself a rank among the world’s dignitaries by such means, to step aside out of the narrow circle in which his claims are recognized, and to find how utterly devoid of all significance, beyond that circle, is all that he achieves, and all he aims at.”
—Nathaniel Hawthorne (1804–1864)