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area among 2 circumferences inside a parallelogram

Source: OLCOMA Costa Rica National Olympiad, Final Round, 2019 3.2

September 21, 2021
geometryparallelogramareas

Problem Statement

Consider the parallelogram ABCDABCD, with ∠ABC=60\angle ABC = 60 and sides AB=3AB =\sqrt3, BC=1BC = 1. Let ω\omega be the circle of center BB and radius BABA, and let τ\tau be the circle of center DD and radius DADA. Determine the area of the region between the circumferences ω\omega and τ\tau, within the parallelogram ABCDABCD (the area of the shaded region). https://cdn.artofproblemsolving.com/attachments/5/a/02b17ec644289d95b6fce78cb5f1ecb3d3ba5b.png
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