Problem: In triangle ABC, sides a,b and c are opposite angles A,B and C respectively. AD bisects angle A and meets BC at D. Then if x=CD and y=BD the correct proportion is
Answer Choices:
A. x/a=a/(b+c)
B. x/b=a/(a+c)
C. y/c=c/(b+c)
D. y/c=a/(b+c)
E. x/y=c/b
Solution:
The bisector of an angle of the triangle divides the opposite sides into segments proportional to the other two sides, i.e., y/c=x/b. It follows that x/b=(x+y)/(b+c)=a/(b+c).