The Nine-Point Circle
Here's another recent theorem. For any triangle, a circle can
be constructed passing through nine special points:
- the midpoints of the three sides (green)
- the feet of the altitudes (turquoise)
- the midpoints of each segment from a vertex to the orthocenter (red)
(An altitude extends from a vertex to the opposite side, and
is perpendicular to that side. It intersects the opposite side at its
foot. The orthocenter is the intersection of
the altitudes.
The following illustration shows the Nine-Point circle Try
dragging the triangle's vertices (if your mouse has more than one
button, use the left one).
Source code
In case you are curious, here is the source code that implements this
figure: NinePtCircle.java
Acknowledgement
David E. Joyce of Clark University has written a much better system
that specializes in demonstrating geometric constructions. When I saw
his system, I realized I could adapt mine to achieve a similar
effect. His Geometry applet is available
here.
Alejo Hausner, CS Department, Princeton University
Last modified: Sat Feb 27 17:59:03 EST 1999