You start on point \(A=(0,0)\) and you want to get to point \(B=(10,1)\). There is a circular object with radius \(2\) blocking your way: it's equation is \((x-n)^2+y^2=4\) for some \(n\in [2,8]\). Let the shortest path from \(A\) to \(B\) such that you do not pass through the circular object have length \(P\). What should \(n\) be such that \(P\) is minimized?
Maybe surprisingly, the answer is not \(n=8\).
You can use Wolfram Alpha to bash it.
Diagram will be added ASAP.