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ASU 020 All Russian MO 1962 9.3 min, max inside a regular pentagon

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June 17, 2019
geometrypentagonminimummaximum

Problem Statement

Given regular pentagon ABCDEABCDE. MM is an arbitrary point inside ABCDEABCDE or on its side. Let the distances ∣MA∣,∣MB∣,...,∣ME∣|MA|, |MB|, ... , |ME| be renumerated and denoted with r1≤r2≤r3≤r4≤r5.r_1\le r_2\le r_3\le r_4\le r_5. Find all the positions of the MM, giving r3r_3 the minimal possible value. Find all the positions of the MM, giving r3r_3 the maximal possible value.
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