D, E and F are the points on sides BC, CA and AB respectively of such that AD bisects , BE bisects and CF bisects . If AB = 5 cm, BC = 8 cm and CA = 4 cm, determine AF, CE and BD.

in⊿ ABC

CF bisects ∠A

∴ AF/FB=AE/AC

AF/5-AF=4/8

2AF=5-AF

2AF+AF=5

3AF=5

AF=5/3 cm

⊿ABC, BE bisects ∠B

∴ AE/AC=AB/BC

4-CE/CE=5/8

5CE=32-8CE

5CE+8CE=32

13CE=32

CE=32/13 cm

Similarly

BD/DC=AB/AC

BD/8-BD=5/4

4BD=40-5BD

4BD+5BD=40

9BD=40

BD=40/9 cm