- 1. If the sides of the Pedal Triangle of a point meet the corresponding sides of a Triangle
at , , and , respectively, then , , meet at a point
common to the Circles and . In other words, is one of the intersections
of the Nine-Point Circle of and the Pedal Circle of .
- 2. If a point moves on a fixed line through the Circumcenter, then its Pedal Circle passes
through a fixed point on the Nine-Point Circle.
- 3. The Pedal Circle of a point is tangent to the Nine-Point Circle Iff the point and its
Isogonal Conjugate lie on a Line through the Orthocenter.
Feuerbach's Theorem is a special case of this theorem.
See also Circumcenter, Feuerbach's Theorem, Isogonal Conjugate, Nine-Point Circle, Orthocenter,
Pedal Circle
References
Johnson, R. A. Modern Geometry: An Elementary Treatise on the Geometry of the Triangle and the Circle. Boston, MA:
Houghton Mifflin, pp. 245-247, 1929.
© 1996-9 Eric W. Weisstein
1999-05-26