Two people walk in concentric circles, their respective positions given by r1(t) = 10 cos t i + 10 sin t j and r2(t) = 20 cos 2t i + 20 sin 2t j.
(a) Find a parametrization for the path followed by the midpoint of the line segment joining them.
(b) Determine the time at which the midpoint is closest to the origin.
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