Wandering Epicycle

Here is an intriguing problem from the 2021 Math Calendar.

“If the smaller circle of diameter 7 rotates without slipping within the larger circle, what is the length of the path of P?”

The problem did not state clearly how far the smaller circle should rotate.  Its answer implied it should complete just one full (360°) rotation within the larger circle.

Recall that all the answers are integer days of the month.

See the Wandering Epicycle

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