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)
Answer & explanation
Correct answer: option 3
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