Let \( C \) be the circle \( x^{2}+y^{2}=1 \) in the \( x y \)-plane. For each \( t \geq \) 0 , ...

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Let \( C \) be the circle \( x^{2}+y^{2}=1 \) in the \( x y \)-plane. For each \( t \geq \) 0 , let \( L_{t} \) be the line passing through \( (0,1) \) and \( (t, 0) \). Note that \( L_{t} \) intersects \( C \) in two points, one of which is \( (0,1) \). Let \( Q_{1} \) be the other point. As \( t \) varies between 1 and \( 1+\sqrt{2} \), the - collection of points \( Q_{1} \) sweeps out an arc on \( C \). The angle subtended by this arc at \( (0,0) \) is
(a) \( \frac{\pi}{8} \)
(b) \( \frac{\pi}{4} \)
(c) \( \frac{\pi}{3} \)
(d) \( \frac{3 \pi}{8} \)
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