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chord rotates inside a 17-gon 2019 BMT Individual 11

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January 5, 2022
geometryrotationpolygon

Problem Statement

A regular 1717-gon with vertices V1,V2,...,V17V_1, V_2, . . . , V_{17} and sides of length 33 has a point P P on V1V2V_1V_2 such that V1P=1V_1P = 1. A chord that stretches from V1V_1 to V2V_2 containing P P is rotated within the interior of the heptadecagon around V2V_2 such that the chord now stretches from V2V_2 to V3V_3. The chord then hinges around V3V_3, then V4V_4, and so on, continuing until P P is back at its original position. Find the total length traced by P P.
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