The most important thing in solving any problem is to understand the problem. And in problem like this it is very important that you are able to depict the problem in a simple line drawing (2-D) accurately and clearly.
Note the problem says the rod is touching the cylinder at point C, but it doesn’t say that it is the center of the uniform rod.
We have here two objects: the cylinder and the rod; both of them resting on the table below. However the questions ask about the forces that act on the rod. So draw the ‘free body diagram’ for the rod, i.e. show all the forces acting on the rod. The cylinder is smooth but the table is not.