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BMT 2022 Geometry #3 / General #18

Source:

August 12, 2023
geometry

Problem Statement

Let equilateral triangle △ABC\vartriangle ABC be inscribed in a circle ω1\omega_1 with radius 44. Consider another circle ω2\omega_2 with radius 22 internally tangent to ω1\omega_1 at AA. Let ω2\omega_2 intersect sides AB‾\overline{AB} and AC‾\overline{AC} at DD and EE, respectively, as shown in the diagram. Compute the area of the shaded region. https://cdn.artofproblemsolving.com/attachments/a/5/8255cdb8b041719d735607da8139aa4016375d.png
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