0Đ.BP2 ( DO MP = NP )C, DO ∆AMP ~ ∆PNB => AMMP =PNNB => AM.NB...

1, - DE DAP AN THI HSG TOAN 67 8 HUYEN THANH OAI
Lớp 6 Toán DE DAP AN THI HSG TOAN 67 8 HUYEN THANH OAI

1,0đ.

BP

2

( do MP = NP )

c, Do ∆AMP ~ ∆PNB =>

AMMP =PNNB

=> AM.NB = MP.PN = MP

2

=> AM.NP = CM

2

– CP

2

= ( CA–AM )(CB–BN ) – CP

2

= CA.CB – CA.BN – AM.CB + AM.BN – CP

2

=> AM.CB + BN.CA+ CP

2

= CA.CB

0,5đ.

=> AM.CB.AB + BN.CA.AB + CP

2

.AB = AB.BC.CA (1)

Từ cõu (b) cú :

AMAP =APAB

-> AM.AB = AP

2

(2)

BNBP =BPAB

-> BN.AB = BP

2

(3)

Từ (1), (2), (3) ->đpcm