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\begin{document}

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\begin{center}
{\Large NMU Math \& CS Department} \\
\vspace{0.5cm}
{\Large Problem of the Month, December 2023}
\end{center}

\vspace{1cm}

\paragraph{} Imagine a circle of radius $10$ containing a smaller circle of radius $7$ tangent to it.

\paragraph{} Now imagine rolling the smaller circle along the circumference of the larger circle for one complete traverse of the circumference of the larger circle (without any sliding or slipping).

\begin{center}
\begin{tikzpicture}[scale=2]
\draw[thick] (0.36,-0.2) circle (1.43);
\filldraw[fill=black!3,thick](0,0) circle (1);
\end{tikzpicture}
\end{center}

\paragraph{} Relative to an external observer, what is the total observed rotation of the smaller circle (about its center, measured in degrees)? Explain your work.
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