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# Pedal Circle

The pedal circle with respect to a pedal point of a triangle is the circumcircle of the pedal triangle with respect to . Amazingly, the vertices of the pedal triangle of the isogonal conjugate point of also lie on the same circle (Honsberger 1995). If the pedal point is taken as the incenter, the pedal circle is given by the incircle.

The radius of the pedal circle of a point is

(Johnson 1929, p. 141).

When is on a side of the triangle, the line between the two perpendiculars is called the pedal line. Given four points, no three of which are collinear, then the four pedal circles of each point for the triangle formed by the other three have a common point through which the nine-point circles of the four triangles pass.

Fontené Theorems, Griffiths' Theorem, Miquel Point, Nine-Point Circle, Pedal Line, Pedal Triangle

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## References

Coolidge, J. L. A Treatise on the Geometry of the Circle and Sphere. New York: Chelsea, p. 50, 1971.Fontené, G. "Sur le cercle pédal." Nouv. Ann. Math. 65, 55-58, 1906.Honsberger, R. More Mathematical Morsels. Washington, DC: Math. Assoc. Amer., p. 54, 1991.Honsberger, R. "The Pedal Circle." §7.4 (viii) in Episodes in Nineteenth and Twentieth Century Euclidean Geometry. Washington, DC: Math. Assoc. Amer., pp. 67-69, 1995.Johnson, R. A. Modern Geometry: An Elementary Treatise on the Geometry of the Triangle and the Circle. Boston, MA: Houghton Mifflin, 1929.

Pedal Circle

## Cite this as:

Weisstein, Eric W. "Pedal Circle." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/PedalCircle.html