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UKMT Senior Mathematical Challenge, 2021

Geometry Difficulty 3.0 AMC 10/12 Find the answer United Kingdom

A triangle with interior angles $60^\circ$ , $45^\circ$ and $75^\circ$ is inscribed in a circle of radius $2$ . What is the area of the triangle?

(A) $2\sqrt{3}$ (B) $4$ (C) $6 + \sqrt{3}$ (D) $6\sqrt{3}$ (E) $3 + \sqrt{3}$

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