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UKMT Pink Kangaroo, 2019

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

A square has two of its vertices on a semicircle and the other two on the diameter of the semicircle as shown. The radius of the circle is $1$ . What is the area of the square?

(A) $\dfrac{4}{5}$ (B) $\dfrac{\pi}{4}$ (C) $1$ (D) $\dfrac{4}{3}$ (E) $\dfrac{2}{\sqrt{3}}$

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