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max area of triangle with vertices on concentric circles 2020 PUMaC Team 7

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January 1, 2022
geometryareasgeometric inequalityarea of a triangle

Problem Statement

Let X,YX, Y , and ZZ be concentric circles with radii 11, 1313, and 2222, respectively. Draw points A,BA, B, and CC on XX, YY , and ZZ, respectively, such that the area of triangle ABCABC is as large as possible. If the area of the triangle is Δ\Delta, find Δ2\Delta^2.
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