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?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 3 : 4.
In triangle ABC, the bisector of angle BAC cuts the line BC at D.
BD = 6 and BC = 14
The angle bisector of a triangle divides the opposite side into two parts proportional to the other two sides of the triangle.
DC = BC - BD = 14 - 6 = 8cm
According to the Angle Bisector Theorem
BD / CD = AB / AC
⇒ 6/8 = AB / AC
⇒ AB / AC = 3/A
The value of AB: AC is 3 : 4.