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AMC 12B 2025 (Problem 16)

An analog clock starts at midnight and runs for 20252025 minutes before stopping. What is the tangent of the acute angle between the hour hand and the minute hand when the clock stops?
(A)  0\text{(A)}\;0(B)  2−1\text{(B)}\;\sqrt2-1(C)  2−2\text{(C)}\;2-\sqrt2(D)  22\text{(D)}\;\frac{\sqrt2}{2}(E)  3−2\text{(E)}\;3-\sqrt2