In triangle ABC, the bisector of angle BAC cuts the line BC at D. If BD = 6 and BC = 14 then what is the value of AB : AC?

3 : 4

In triangle ABC, the bisector of angle BAC cuts the line BC at D.

BD = 6 and BC = 14 

DC = BC - BD  = 14 - 6 = 8 cm

According to the Angle Bisector Theorem,

\(\frac{BD}{CD}\) = \(\frac{AB}{AC}\)

⇒ \(\frac{6}{8}\) = \(\frac{AB}{AC}\)

⇒ AB : AC = 3 : 4