A circle $S $ with arbitrary radius and center is given. Let point $P $ be in the exterior of the circle $S $ and draw the two tangent lines from the point $P $ to the circle $S $. Let the point $A $ be in the circumference of the circle $S $ and let the points $B, C$ be on the two tangent lines. Find the minimum value of the perimeter of the triangle formed by the points $A, B, C $.
My attempt I considered the points $A', A"$ which are formed by the symmetry about the two tangent lines from the point $A$ but can't proceed further. Any help would be appreciated.