Round & Round, It Goes

Geometry Level 3

A coin of diameter 1 cm rolls from point \(B\) along the (solid) arc of a big circle and reaches point \(A\) after revolving 8 full rounds.

If the (red) line segment \(AB\) is 24 cm long, how many rounds in total will this coin need to revolve to complete one full circle (from B back to B)?

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