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UKMT Senior Mathematical Challenge, 2025

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

The diagram shows a square, one of its diagonals and a circle. The circle touches the diagonal and two sides of the square. The circle has radius 2. What is the length of the side of the square?

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

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