Given any Triangle , the signed sum of Perpendicular distances from the Circumcenter
to the sides is
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.