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Bosnia and Herzegovina TST 1998 Day 1 Problem 1

Source: Bosnia and Herzegovina Team Selection Test 1998

September 20, 2018
circledistancemaximum and minimumgeometry

Problem Statement

Let P1P_1, P2P_2, P3P_3, P4P_4 and P5P_5 be five different points which are inside DD or on the border of figure DD. Let M=min{PiPj∣i≠j}M=min\left\{P_iP_j \mid i \neq j\right\} be minimal distance between different points PiP_i. For which configuration of points PiP_i, value MM is at maximum, if : a)a) DD is unit square b)b) DD is equilateral triangle with side equal 11 c)c) DD is unit circle, circle with radius 11
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