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2022 PUMaC Geometry A3 / B5

Source:

September 10, 2023
geometry

Problem Statement

Daeun draws a unit circle centered at the origin and inscribes within it a regular hexagon ABCDEFABCDEF. Then Dylan chooses a point PP within the circle of radius 22 centered at the origin. Let MM be the maximum possible value of ∣PA∣⋅∣PB∣⋅∣PC∣⋅∣PD∣⋅∣PE∣⋅∣PF∣|PA| \cdot |PB| \cdot |PC| \cdot |PD| \cdot |PE| \cdot |PF|, and let NN be the number of possible points PP for which this maximal value is obtained. Find M+N2M + N^2.
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