SOLUTION: in triangle ABC, BD is the angle bisector of angle B. if AB=6 and BC=8, find the ratio AD:DC.

Algebra ->  Triangles -> SOLUTION: in triangle ABC, BD is the angle bisector of angle B. if AB=6 and BC=8, find the ratio AD:DC.      Log On


   

Question 24465: in triangle ABC, BD is the angle bisector of angle B. if AB=6 and BC=8, find the ratio AD:DC.
Answer by venugopalramana(3286) About Me  (Show Source):
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SEE THE FOLLOWING EXAMPLE AND YOU CAN SOLVE YOUR PROBLEM YOUR SELF
IN A TRIANGLE THE ANGLE BISECTOR OF ANY ANGLE DIVIDES THE OPPOSITE SIDE IN THE RATIO OF 2 ADJACENT SIDES OF THE TRIANGLE
HERE EFG IS A TRIANGLE, FH is the bisector of angle F.IT MEETS THE OPPOSITE SIDE EG AT H.HENCE AS PER THE THEOREM WE HAVE
EH/HG=FE/FG
if EH=6 and HG= 9,
HENCE EH/HG=6/9=FE/FG
FG/FE=9/6=3/2
the ratio of FG:EF=3:2