Editing Nine-point circle (section)

==Nine Significant Points of Nine Point Circle==

[[File:Nine-point circle.svg]]

The diagram above shows the nine significant points of the nine-point circle. Points {{mvar|D, E, F}} are the midpoints of the three sides of the triangle. Points {{mvar|G, H, I}} are the feet of the altitudes of the triangle. Points {{mvar|J, K, L}} are the midpoints of the line segments between each altitude's [[vertex (geometry)|vertex]] intersection (points {{mvar|A, B, C}}) and the triangle's orthocenter (point {{mvar|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.