Angle Bisector Problem

[llooppii]

Prove that the interior bisectors of two of the angles of a non-isosceles triangle and the exterior bisector of the third angle meet the sides of the triangle in three collinear points.

Any advice you can give is great. What I am particularly having trouble with is how I can prove that the points are collinear. The points from the interior bisectors are collinear because they meet at a common point, but how does the other point become collinear?

 

[tkhunny]

First, why is an exterior bisector different from an interior bisector?

Second, "meet the sides of the triangle in three collinear points". Are you sure this is correct? To do this on the "sides of the triangle", it must be all on the same side. Of course, if this is the intent, than collinear is easy enough to show.