A friend recently emailed me this one (apparently it's from a game he plays)
AB=81, AD=180, AE=108, BE=135,CD=84, CE=156, BC=square root of ?
I've been poring over this for a bit, but I'm obviously out of practice.
Anyone care to have a bash?
If that is the case, then ABE is a right-angled triangle, because . However, the remaining information is not sufficient to fix the positions of C and D. You need an extra piece of information, such as the distance DE, before you can pin down the distance BC.