∴DM/CM=BM/AM (parallel lines are cut according to the proportion of corresponding line segments)

∴DM=5×4.5/3=7.5

Similarly, CM/CD=EK/EF.

∴4.5/ 12=EK/ 16

EK=4.5× 16/ 12=6

∴KF=EF-EK= 10

9. It is proved that if the extension line from CE‖AD to BA is at point E, then ∠BDA=∠BCE, ∠BAD=∠E, ∠ACE=∠CAD.

∴△BAD∽△BEC

∴BD/BC=AB/BE

∴BD/(BC-BD)=AB/(BE-AB)

That is BD/DC=AB/AE.

∵AD is the bisector of∝∠ ∝∠BAC.

∴∠BAD=∠CAD= 1/2∠BAC

∴∠ACE=∠E

∴AC=AE

∴AB/AC=BD/DC