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 : DC?
Option 1: 10 : 7
Option 2: 5 : 7
Option 3: 7 : 5
Option 4: 7 : 10
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Correct Answer: 5 : 7
Solution :
In a triangle, the ratio of the sides is equal to the ratio of the segments determined by the angle bisector. This is known as the Angle bisector theorem.
So, in triangle ABC, if AD is the bisector of angle BAC,
$⇒\frac{AB}{AC} = \frac{BD}{DC}$
Given that AB = 10 cm and AC = 14 cm,
$⇒\frac{10}{14} = \frac{BD}{DC}$
$⇒\frac{5}{7} = \frac{BD}{DC}$
$\therefore\frac{BD}{DC}=\frac{5}{7}$
Hence, the correct answer is 5 : 7.
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