Question 22A circle of radius $r$ is surrounded by three circles, whose radii are $1,$ $2,$ and $3,$ all externally tangent to the inner circle and externally tangent to each other, as shown in the diagram below. What is $r?$$\dfrac{1}{4}$$\dfrac{6}{23}$$\dfrac{3}{11}$$\dfrac{5}{17}$$\dfrac{3}{10}$
