All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Shapes > Geometry
Triangular Billiard Table (Posted on 2005-05-12) Difficulty: 3 of 5
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?

See The Solution Submitted by Bractals    
Rating: 2.5000 (2 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
What I've found | Comment 3 of 9 |

Just playing around with Geometer's sketchpad.  The value of the tan(BAD) seems to be able to take on any value from 0 to about .42

The former when tan(BAC) is 0 the latter when tan(BAC) is around .61

I don't see any connection with the way tan(BAD) changes and any other quantity.  Am I missing something?

Oops!  I am.  I wasn't forcing the ball to end up at B.

Playing some more.   tan(BAD) is about .58 and tan(BAC) is around 1/3

I'll try for a proof, but I don't know if I can.

  Posted by Jer on 2005-05-12 18:44:13
Please log in:
Remember me:
Sign up! | Forgot password

Search body:
Forums (1)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (5)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Copyright © 2002 - 2019 by Animus Pactum Consulting. All rights reserved. Privacy Information