Current location - Plastic Surgery and Aesthetics Network - Plastic surgery and beauty - ( 1999? Hangzhou) as shown in the figure, in △ABC, AM and BN intersect at D, BM=3MC, AD=DM, and find the value of: (1) BD: DN; (2) area S△ABN:
( 1999? Hangzhou) as shown in the figure, in △ABC, AM and BN intersect at D, BM=3MC, AD=DM, and find the value of: (1) BD: DN; (2) area S△ABN:
Solution: Solution: (1) Let c be the extension line of point E where CE∨AM intersects BA, and point F where BN intersects Ce.

∫CE∨AM,

∴∠DAN=∠FCN,∠ADN=∠CFN,

∴△DAN∽△FCN,

∴DNFN=ADCF,

And ∵AD=DM,

∴DNFN=DMCF,

∫CE∨AM,

∴BDBF=DMFC=BMBC=34,

∴DNFN=34,

∴BD:DN=3:37=7: 1.

(2) From (1):△ Dan is similar to △FCN.

∴ANCN=DNFN=34

∴S△ABN:S△CBN=AN:CN=3:4.