Question : In triangle ABC, the bisector of angle BAC cuts the side BC at D. If AB = 10 cm, and AC = 14 cm then what is BD : BC ?
Option 1: 5 : 3
Option 2: 7 : 5
Option 3: 5 : 2
Option 4: 5 : 7
Correct Answer: 5 : 7
Solution :
The angle bisector of a triangle divides the opposite side into two parts proportional to the other two sides of the triangle.
According to the concept,
$\frac{AB}{AC} = \frac{BD}{DC}$
⇒ $\frac{10}{14} = \frac{BD}{DC}$
⇒ $\frac{5}{7} = \frac{BD}{DC}$
$\therefore BD:DC=5:7$
Hence, the correct answer is 5 : 7.
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