Clock hands: arcs, swept area and a right angle

A clock has a minute hand of length \(12\) cm and an hour hand of length \(8\) cm. Assume both hands move steadily.

1. Find the exact distance travelled by the tip of the minute hand from \(12{:}00\) to \(12{:}20\), and the exact area swept by the minute hand in that time.[2]
2. Find the exact distance between the tips of the hands at \(3{:}00\).[2]
3. Find the first time after \(12{:}00\) at which the hands are at right angles, giving your answer to the nearest second.[3]