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maximum length of vector

Source: Romanian NMO 2021 grade 9 P2

April 15, 2023
vectorgeometrytrigonometry

Problem Statement

Let P0,P1,…,P2021P_0, P_1,\ldots, P_{2021} points on the unit circle of centre OO such that for each n∈{1,2,…,2021}n\in \{1,2,\ldots, 2021\} the length of the arc from Pn−1P_{n-1} to PnP_n (in anti-clockwise direction) is in the interval [π2,π]\left[\frac{\pi}2,\pi\right]. Determine the maximum possible length of the vector: OP0→+OP1→+…+OP2021→.\overrightarrow{OP_0}+\overrightarrow{OP_1}+\ldots+\overrightarrow{OP_{2021}}.
Mihai Iancu
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