Proving Angle Bisector Problem in Non-Isosceles Triangle

[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.


I hope this is posted in the right area because it is concerning geometry!

I've been trying at this for a few days and can't make any progress. I understand that the two points formed from the interior bisectors are collinear, but that really doesn't help because any points two points are collinear. So any help is appreciated.

 

[hunt_mat]

The rought and ready answer is to split the triangle up into very tiny rectangles, the centra of gravity (which is what your asking for really) will be in the middle of each of these very thin rectangles.

Do this for all three sides to obtain the answer.

Mat