Bouncing in a U-Shaped Gallery

Consider the U-shaped hallway illustrated above. All angles are right angles and the numbers indicate the lengths of various walls. The figure is not drawn to scale.

The problem is to send a point sized billiard ball located at the red dot in the lower left corner of the upper hallway, to the blue dot in the upper left corner of the lower hallway. Assume that the billiard ball reflects with equal angles off of walls. If the ball goes into a corner, its velocity is reversed. Also assume that if the ball goes through a corner but not into a corner, it skims right on by.

Many paths are possible. Which minimizes distance and what is this minimum distance?

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