In Δ ABC with sides 6 cm, 9 cm and 10 cm, the angle bisector of the largest angle divides the opposite side into two segments. What is the length of the shorter segment? (in cm)

2 2.5 4 5.5

4

By interior angle bisector theorem ⇒ Angle bisector divides opposite side in the ratio of remaining two sides. Therefore, BD : DC = 6 : 9 ⇒ 2 : 3 Smaller side = \(\frac{2}{5}\) ×10 = 4 cm