Problem: In triangle ABC,AL bisects angle A and CM bisects angle C. Points L and M are on BC and AB, respectively. The sides of triangle ABC are a,b, and c. Then MBAM​=kLBCL​ where k is:
Answer Choices:
A. 1
B. a2bc​
C. bca2​
D. bc​
E. ac​
Solution:
The bisector of an angle of a triangle divides the opposite sides into segments proportional to the other two sides, therefore, MBAM​=ab​ and LBCL​=cb​.
Since ac​⋅cb​=ab​,k=ac​.