A circle of radius $r$ is surrounded by $12$ circles of radius $1,$ externally tangent to the central circle and sequentially tangent to each other, as shown. Then $r$ can be written as $\sqrt a + \sqrt b + c,$ where $a, b, c$ are integers. What is $a+b+c?$ $\textbf{(A) } 3 \qquad$ $ \textbf{(B) } 5 \qquad$ $ \textbf{(C) } 7 \qquad$ $ \textbf{(D) } 9 \qquad$ $ \textbf{(E) } 11$