In ΔABC with sides 8 cm, 9 cm and 34 cm, the angle bisector of the largest angles divides the opposite sides into two segments.  What is the length of the shorter segment?

16

*(The largest angle is always opposite to the larges side of the triangle)

*(By Interior angle bisector theorem:- Angle bisector divides opposite side in the ratio of remaining two sides)

AD : DC = 8 : 9

∴ AC = AD + DC = 8 + 9 = 17

Shorter segment = \(\frac{8}{17}\) × 34 = 16 cm