Angle Bisector Theorem
The Angle Bisector Theorem gives information about ratios of side length in a triangle when an angle bisector is drawn. https://en.wikipedia.org/wiki/Angle_bisector_theorem gives the theorem. A question like this appeared in 1966, http://artofproblemsolving.com/wiki/index.php?title=1966_AHSME_Problems/Problem_11