Let n be a positive integer. Let P,Q,A1,A2,...,An be distinct points such that A1,A2,...,An are not collinear. Suppose that PA1+PA2+...+PAn, and QA1+QA2+...+QAn, have a common value s for some real number s. Prove that there exists a point R such that RA1+RA2+...+RAn<s. geometryGeometric Inequalities