Let \( A B C D \) be a square of side length 1 and a circle passing through \( B \) and \( C \),...

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Let \( A B C D \) be a square of side length 1 and a circle passing through \( B \) and \( C \), and touching \( A D \). The radius of is
(a) \( \frac{3}{8} \)
(b) \( \frac{1}{2} \)
(c) \( \frac{1}{\sqrt{2}} \)
(d) \( \frac{5}{8} \)
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