Circle Time

Three circles of different radii each touch the other two. What can you deduce about the arc length between these points?
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Three circles $C_1$, $C_2$ and $C_3$, of radii 1 cm, 2 cm and 3 cm respectively touch as shown. $C_1$ meets $C_2$ at $P$ and meets $C_3$ at $Q$.

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Circle Time


What is the length in cm of the longer arc of circle $C_1$ between $P$ and $Q$?

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.