Reflection across a Cylinder

A reflective cylinder of radius $5$ has its axis passing through the point $( 0, 0, 3 )$ , and parallel to the vector $(-1, -1, 2 )$ . A light source is placed at point $A(45,0,0)$ . A light ray radiating from $A$ is to reflect off the surface of the cylinder, at a point $C (x,y,z)$ , into point $B(30, 40, 0)$ . Find $x + y + z$ . Note that point $C$ is the point on the surface of the cylinder that minimizes the sum of distances $AC + CB$ .