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SMT 2018 Geometry #4 regular dodecagon

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August 8, 2023
geometry

Problem Statement

Let a1,a2,...,a12a_1, a_2, ..., a_{12} be the vertices of a regular dodecagon D1D_1 (1212-gon). The four vertices a1a_1, a4a_4, a7a_7, a10a_{10} form a square, as do the four vertices a2a_2, a5a_5, a8a_8, a11a_{11} and a3a_3, a6a_6, a9a_9, a12a_{12}. Let D2D_2 be the polygon formed by the intersection of these three squares. If we let[A] [A] denotes the area of polygon AA, compute [D2][D1]\frac{[D_2]}{[D_1]}.
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