Carnot's Theorem
Given any Triangle 
, the signed sum of Perpendicular distances from the Circumcenter 
to the sides is
where
is the Inradius and 
is the Circumradius. The sign of the distance is chosen to be PositiveIff the entire segment 
lies outside the Triangle.See also Japanese Triangulation Theorem
References
Eves, H. W. A Survey of Geometry, rev. ed. Boston, MA: Allyn and Bacon, pp. 256 and 262, 1972. Honsberger, R. Mathematical Gems III. Washington, DC: Math. Assoc. Amer., p. 25, 1985.
- Lebesgue Measurability Problem
- Lebesgue Measure
- Lebesgue Minimal Problem
- Lebesgue-Radon Integral
- Lebesgue Singular Integrals
- Lebesgue-Stieltjes Integral
- Lebesgue Sum
- Le Cam's Identity
- Leech Lattice
- Lefshetz Fixed Point Formula
- Lefshetz's Theorem
- Lefshetz Trace Formula
- Leg
- Legendre Addition Theorem
- Legendre Differential Equation
- Legendre Duplication Formula
- Legendre Function of the First Kind
- Legendre Function of the Second Kind
- Legendre-Gauss Quadrature
- Legendre-Jacobi Elliptic Integral
- Legendre Polynomial
- Legendre Polynomial of the Second Kind
- Legendre Quadrature
- Legendre Relation
- Legendre's Chi-Function