Question

In \( \triangle ABC \), \( AD \) is the bisector of \( \angle BAC \). If \( AB = 4 \, \text{cm} \), \( AC = 6 \, \text{cm} \), and \( BD = 2 \, \text{cm} \), then the value of \( DC \) is:

• A. 3 cm
• B. 6 cm
• C. 7 cm
• D. 4 cm

Hint:

The angle bisector theorem states that the angle bisector divides the opposite side in the ratio of the adjacent sides.

Answer 1

The Correct Option is A

By the angle bisector theorem, the angle bisector divides the opposite side in the ratio of the adjacent sides. Thus: \[ \frac{AB}{AC} = \frac{BD}{DC}. \] Substitute the given values: \[ \frac{4}{6} = \frac{2}{DC} \quad \Rightarrow \quad DC = \frac{6 \times 2}{4} = 3. \] Thus, the correct answer is \( \boxed{3} \).