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UKMT Senior Mathematical Challenge, 2019

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

Two circles of radius $1$ are such that the centre of each circle lies on the other circle. A square is inscribed in the space between the circles. What is the area of the square?

(A) $2 - \frac{\sqrt{7}}{2}$ (B) $2 + \frac{\sqrt{7}}{2}$ (C) $4 - \sqrt{5}$ (D) $1$ (E) $\frac{\sqrt{5}}{5}$

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