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.