2016 Fermat Problem 23

Seven coins of three different sizes are placed flat on a table, arranged as shown in the diagram. Each coin, except the centre one, touches three other coins. The centre coin touches all of the other coins. If the coins labelled C_3 have a radius of 3 cm, and those labelled C_2 have radius 2 cm, then the radius of the coin labelled X is closest to

\textbf{(A)}\ 0.615 \text{ cm}\quad \textbf{(B)}\ 0.620 \text{ cm}\quad \textbf{(C)}\ 0.610 \text{ cm}\quad \textbf{(D)}\ 0.605 \text{ cm}\quad \textbf{(E)}\ 0.625 \text{ cm}

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

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