MathDB

17

Part of 1983 IMO Shortlist

Problems(1)

Distance of points

Source:

9/9/2010
Let P1,P2,…,PnP_1, P_2, \dots , P_n be distinct points of the plane, n≥2n \geq 2. Prove that max⁡1≤i<j≤nPiPj>32(n−1)min⁡1≤i<j≤nPiPj \max_{1\leq i<j\leq n} P_iP_j > \frac{\sqrt 3}{2}(\sqrt n -1) \min_{1\leq i<j\leq n} P_iP_j
geometrygeometric inequalityoptimizationminimizationmaximizationIMO Shortlistpoint set