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:
“Wise child, didst hastily return
And mad’st thy mother’s womb thine urn.
How summed a circle didst thou leave mankind
Of deepest lore, could we the center find!”
—Ben Jonson (1572–1637)