In ∆ABC, AB = 6 cm, BC = 9 cm, and CA = 12 cm, If AD is the angle bisector of ∠BAC, D is a point on BC, then find DC
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 6
The Angle Bisector Theorem states that the angle bisector of an angle in a triangle divides the opposite side in the same ratio as the sides containing the angle.
AB = 6 cm, AC = 12 cm, and BC = 9 cm
Let DC = x cm
Then BD = (9 - x)
Here, BD/DC = AB/AC
⇒ (9 - x)/x = 6/12 = 1/2
⇒ x = 18 - 2x
⇒ 3x = 18
⇒ x = 18/3 = 6
Therefore, the length of DC is 6 cm.