Significant Nine Points
The diagram above shows the nine significant points of the nine-point circle. Points D, E, and F are the midpoints of the three sides of the triangle. Points G, H, and I are the feet of the altitudes of the triangle. Points J, K, and L are the midpoints of the line segments between each altitude's vertex intersection (points A, B, and C) and the triangle's orthocenter (point S).
For an acute triangle, six of the points (the midpoints and altitude feet) lie on the triangle itself; for an obtuse triangle two of the altitudes have feet outside the triangle, but these feet still belong to the nine-point circle.
Read more about this topic: Nine-point Circle
Famous quotes containing the words significant and/or points:
“By degrees we may come to know the primitive sense of the permanent objects of nature, so that the world shall be to us an open book, and every form significant of its hidden life and final cause.”
—Ralph Waldo Emerson (1803–1882)
“Wi’ joy unfeigned brothers and sisters meet,
An’ each for other’s weelfare kindly spiers:
The social hours, swift-winged, unnoticed fleet;
Each tells the uncos that he sees or hears;
The parents, partial, eye their hopeful years;
Anticipation forward points the view:”
—Robert Burns (1759–1796)