easy little geometry problem

[futurebird]

Okay, I’m still thinking about my constrained version of the traveling salesmen problem. Here is an easy little geometry problem:

Triangle ABC has sides:

AB = p
BC = q
CA = r

Triangle ABD has sides

AB = p (duh)
BD = s
AD = t

Express the two possible lengths of DC in terms of p, q r, s and t

I’ve done it one way, but it looks like a big mess.