Find the length of the line that connects Cylinder's bases 
Points $A$ and $B$ are on different bases of the Cylinder. Line $AB$ is on plane $\alpha$, which is parallel to Cylinder's axis. Find the length of line $AB$, if it creates $45^\circ$ angle with the base of the cylinder. Also, cylinder's base has radius $=5$, the distance from the Cylinder's axis to the plane $\alpha$ is $4$.

I translated this problem, so if anything's ambiguous please do comment.
The picture wasn't given, but here's my best attempt (interpretation):

The dotted line is supposed to be a plane... The perpendicular line is the distance from the the axis to the plane $\alpha$, since it's parallel to the axis, the perpendicular will just lie on the base of the cylinder.. Correct me if i'm wrong here.
So after that, I couldn't really go anywhere, As far as i'm concerned, A and B could be anywhere on the bases... Please try to provide a geometrical view / explanation.

So far as I understood the plane parallel to cylinder axis cuts the cylinder at 4 distance units away, making a rectangular shaped intersection area width 6 units in the base plane. Line $AB$ makes minimum $45^{\circ}$ angle to its projection ( or width of rectangle, but not radius!) in this plane of intersection.

So $AB= 6 \sqrt{2}.$
