**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 points and/or significant:

“There are good *points* about all such wars. People forget self. The virtues of magnanimity, courage, patriotism, etc., etc., are called into life. People are more generous, more sympathetic, better, than when engaged in the more selfish pursuits of peace.”

—Rutherford Birchard Hayes (1822–1893)

“Is it impossible not to wonder why a movement which professes concern for the fate of all women has dealt so unkindly, contemptuously, so destructively, with so *significant* a portion of its sisterhood. Can it be that those who would reorder society perceive as the greater threat not the chauvinism of men or the pernicious attitudes of our culture, but rather the impulse to mother within women themselves?”

—Elaine Heffner (20th century)