MathDB

7

Part of 2020 Princeton University Math Competition

Problems(1)

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

Source:

1/1/2022
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.
geometryareasgeometric inequalityarea of a triangle