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: 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 Web Resource. https://mathworld.wolfram.com/RadonsTheorem.html