MathDB
Point inside a Pentagon

Source: 1962 All-Soviet Union Olympiad

January 15, 2018
Russiageometry

Problem Statement

Given is a fixed regular pentagon ABCDEABCDE with side 11. Let MM be an arbitrary point inside or on it. Let the distance from MM to the closest vertex be r1r_1, to the next closest be r2r_2 and so on, so that the distances from MM to the five vertices satisfy r1≤r2≤r3≤r4≤r5r_1\le r_2\le r_3\le r_4\le r_5. Find (a) the locus of MM which gives r3r_3 the minimum possible value, and (b) the locus of MM which gives r3r_3 the maximum possible value.
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