2023 Pascal Problem 20

Four larger circles with radius 5 are arranged so that their centres are the vertices of a square. Each of the larger circles is tangent to (that is, just touches) two of the other circles, as shown. A smaller circle with radius r is drawn in the region between the four larger circles. The smaller circle is tangent to each of the larger circles. The value of r is closest to

\textbf{(A)}\ 1.9\quad \textbf{(B)}\ 2.0\quad \textbf{(C)}\ 2.1\quad \textbf{(D)}\ 2.2\quad \textbf{(E)}\ 2.3

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Pascal contests here.