I'm not sure but when you have two external angle bisectors, they intersect at a point which is the center of the excircles.
Excircles -- from Wolfram MathWorld
This might help you.
Use Ceva's Theorem to prove that the external bisectors of two angles of a triangle and the internal bisector of the third angle are concurrent.
Any hints on where to begin would be greatly appreciated.
I'm not sure but when you have two external angle bisectors, they intersect at a point which is the center of the excircles.
Excircles -- from Wolfram MathWorld
This might help you.