Radon's theorem states that any set of 
points in 
can always be partitioned in two subsets 
and 
such that the convex hulls
of 
and 
intersect.
Radon's Theorem
See also
Convex HullExplore with Wolfram|Alpha
References
Eckhoff, J. "Helly, Radon, and Carathéodory Type Theorems." Ch. 2.1 in Handbook of Convex Geometry (Ed. P. M. Gruber and J. M. Wills). Amsterdam, Netherlands: North-Holland, pp. 389-448, 1993.McMullen, P. and Shepard, G. C. Convex Polytopes and the Upper Bound Conjecture. London, England: Cambridge University Press, pp. 22-24, 1971.Peterson, B. B. "The Geometry of Radon's Theorem." Amer. Math. Monthly 79, 949-963, 1972.Peyerimhoff, N. "Areas and Intersections in Convex Domains." Amer. Math. Monthly 104, 697-704, 1997.Rado, R. "Theorems on the Intersection of Convex Sets of Points." J. London Math. Soc. 27, 320-328, 1952.Ziegler, G. M. Ex. 6.0 in Lectures on Polytopes. New York: Springer-Verlag, 1994.Referenced on Wolfram|Alpha
Radon's TheoremCite this as:
Weisstein, Eric W. "Radon's Theorem." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/RadonsTheorem.html