11. To Cross any Round Obstacle

Given a circular obstacle described by

$$(x-a)^2+(y-b)^2=r^2,$$

and two points $P_1=(x_1,y_1)$ and $P_2=(x_2,y_2)$ outside the circle, given that line segment P1P2 intersects the interior of the circle, determine the length of the shortest path from $P_1$ to $P_2$ that does not intersect the interior of the circular obstacle. Derive a general expression for this distance.