In ∆ABC, AB = 7cm, BC = 10cm, and AC = 8cm. If AD is the angle bisector of ∠BAC, where D is a point on BC, then (in cm) is equal to:
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e.
Let the BD = x
DC = 10 - x
By angle bisector theorem -
BD/CD = AB/AC
x/(10 - x) = 7/8
8x = 70 - 7x
15x = 70x =14/3 cm
BD = 14/3
DC = 10 - 14/3 = 16/3
DC/4 = 16/12 = 4/3