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UKMT Senior Mathematical Challenge, 2019

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

A circle with radius $1$ touches the sides of a rhombus, as shown. Each of the smaller angles between the sides of the rhombus is $60°$ . What is the area of the rhombus?

(A) $6$ (B) $4$ (C) $2\sqrt{3}$ (D) $3\sqrt{3}$ (E) $\frac{8\sqrt{3}}{3}$

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