We have a billiard table in the shape of a right triangle ABC with B the right angle. A cue ball is struck at vertex A and bounces off sides BC, AC, AB, and AC at points D, E, F, and G respectively ending up at vertex B. Assume the angle of incidence equals the angle of reflection at each bounce. If the path segments AD, EF, and GB are concurrent, then what is the tangent of angle BAD?

Discounting dead rails, a sloped surface, or left-hand english, I can't produce such an angle. I'd be glad to be proven wrong.

If no one is able to produce a solution, I'll try to explain why I think there is no such angle.

Posted by Charley on 2005-05-12 17:48:49