Return to my Mathematics pages
Go to my home page

The Nine Point Circle

© Copyright 2001, Jim Loy

Here is the Nine Point Circle. In any triangle these nine points all lie on a circle (the green circle in the diagram):

• The bases of the three altitudes.
• The midpoints of the three sides.
• The midpoints between the orthocenter (point where the three altitudes meet) and each of the three vertices

Apparently, this fact was discovered by Euler. The center of this circle is on the Euler line (see The Centers of a Triangle), midway between the circumcenter and the orthocenter. The incircle and the nine-point circle are tangent at the Feuerbach point. The radius of the nine point circle is half the radius of the circumcircle.

The diagram was drawn using the program Cinderella.

Return to my Mathematics pages
Go to my home page