Online Geometry
Problem 632: Triangle, Interior and Exterior Angle Bisectors,
Midpoints, Collinear Points. Level: High School, Honors Geometry, College,
Mathematics Education

The figure shows a scalene triangle ABC with the
interior and exterior angle bisectors AA', AA", BB', BB", CC', and CC". Prove that
the midpoints of A'A", B'B", and C'C" are
collinear.