Power (Circle)
The Power of the two points 
and 
with respect to a Circle is defined by
Let 
be the Radius of a Circle and 
be the distance between a point and the circle's center. Then thePower of the point relative to the circle is
If
is outside the Circle, its Power is Positive and equal to the square of the length of the segment from to the tangent to the Circle through . If is inside the Circle, then the Power is Negativeand equal to the product of the Diameters through .The Locus of points having Power 
with regard to a fixed Circle of Radius 
is aConcentric Circle of Radius 
. The Chordal Theorem states that the Locus ofpoints having equal Power with respect to two given nonconcentric Circles is a line called theRadical Line (or Chordal; Dörrie 1965).
References
Coxeter, H. S. M. and Greitzer, S. L. Geometry Revisited. Washington, DC: Math. Assoc. Amer., pp. 27-31, 1967. Dixon, R. Mathographics. New York: Dover, p. 68, 1991. Dörrie, H. 100 Great Problems of Elementary Mathematics: Their History and Solutions. New York: Dover, p. 153, 1965. Johnson, R. A. Modern Geometry: An Elementary Treatise on the Geometry of the Triangle and the Circle. Boston, MA: Houghton Mifflin, pp. 28-34, 1929. Pedoe, D. Circles: A Mathematical View, rev. ed. Washington, DC: Math. Assoc. Amer., pp. xxii-xxiv, 1995.
- Carmichael Number
- Carmichael's Conjecture
- Carmichael Sequence
- Carmichael's Theorem
- Carmichael's Totient Function Conjecture
- Carnot's Polygon Theorem
- Carnot's Theorem
- Carotid-Kundalini Fractal
- Carotid-Kundalini Function
- Carry
- Carrying Capacity
- Cartan Matrix
- Cartan Relation
- Cartan Subgroup
- Cartan Torsion Coefficient
- Cartesian Coordinates
- Cartesian Ovals
- Cartesian Product
- Cartesian Trident
- Cartography
- Cascade
- Casey's Theorem
- Casimir Operator
- Cassini Ellipses
- Cassini Ovals