Abstract: In this paper we have proved that if n+2 spheres in n-dimensional spaces with constant curvature K touch each other externally and if k₁,k₂,……k_n+2 denote their principle curvatures, then the following relationhold.
(???19880202???k_i)²-n???19880202???k_i²=2nK
When K=0 and n=2, We get the original form of Descartes circle theorem.