This looks like an optimalization problem. What you need to do is make a function T(x) for the amount of cable that is needed depending on the "branching distance" x from the origin. Then you need to differentiate that formula, and equal it to 0 to find the extremum of the function. (In this case you'll want a minimum, since you're looking for the least possible amount of cable needed).
In this case, the formula for the amount of cable needed would be
In which 11-x is the amount of cable from Centerville to the branching point, and the other term is the amount of cable from the two branches (using Pythagoras).