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.
- Syntonic Comma
- Syracuse Algorithm
- Syracuse Problem
- System of Differential Equations
- System of Equations
- Syzygies Problem
- Syzygy
- Szilassi Polyhedron
- Szpiro's Conjecture
- Sárközy's Theorem
- T2-Separation Axiom
- Tableau
- Tabu Search
- Tacnode
- Tacpoint
- Tactix
- Tail Probability
- Tait Coloring
- Tait Cycle
- Tait Flyping Conjecture
- Tait's Hamiltonian Graph Conjecture
- Tait's Knot Conjectures
- Takagi Fractal Curve
- Take-Away Game
- Takeuchi Function