The triangle that joins up the centres of the circles has sides of length 3 cm, 4 cm, 5 cm so must be a right angled triangle by the converse of Pythagoras' Theorem. Therefore the length of the longer arc of the circle $C_1$ is $\frac{3}{4} \times 2\pi \times 1 = \frac{3}{2} \pi$ cm.

*This problem is taken from the UKMT Mathematical Challenges.*