The Nine Point Circle

Theorem:  In DABC, let A', B' and C' be the midpoints of the opposite sides; let D, E and F be the feet of the altitudes; let H be the orthocenter, and let a, b and c be the midpoints of AH, BH and CH respectively.  Then the nine points A', B', C', a, b, c, D, E and F all lie on a circle.
This sketch demonstrates this theorem.  The circle drawn is the circle with center the midpoint of A'a and through A'.  Note that it goes through the other seven points, as expected.  Sorry, this page requires a Java-compatible web browser.

This java applet was produced using JavaSketchpad.  The following is the maker's beta on this product:

This is a prototype of JavaSketchpad, a World-Wide-Web component of The Geometer's Sketchpad. Copyright ©1990-1998 by Key Curriculum Press, Inc. All rights reserved. Portions of this work were funded by the National Science Foundation (awards DMI 9561674 & 9623018).

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This page was created November 30th, 1998.