已知B（-2,0）,C（2,0）,点A是Y轴正半轴上一点,CD⊥AC交Y轴于D,M为AC上一动点,N为AB延长线一动点,且满足AM+AN=2AC,MN交BC于E,连DE.(3)在（2)的条件下问BC分之EK的值是否发生变化,若不变,求其值.

已知B（-2,0）,C（2,0）,点A是Y轴正半轴上一点,CD⊥AC交Y轴于D,M为AC上一动点,N为AB延长线一动点,且满足AM+AN=2AC,MN交BC于E,连DE.(3)在（2)的条件下问BC分之EK的值是否发生变化,若不变,求其值.
已知B（-2,0）,C（2,0）,点A是Y轴正半轴上一点,CD⊥AC交Y轴于D,M为AC上一动点,N为AB延长线一动点,且满足AM+AN=2AC,MN交BC于E,连DE.(3)在（2)的条件下问BC分之EK的值是否发生变化,若不变,求其值.

已知B（-2,0）,C（2,0）,点A是Y轴正半轴上一点,CD⊥AC交Y轴于D,M为AC上一动点,N为AB延长线一动点,且满足AM+AN=2AC,MN交BC于E,连DE.(3)在（2)的条件下问BC分之EK的值是否发生变化,若不变,求其值.
（1）作辅助线,连接DM,BD,过点N作NL 垂直于AC,交x轴点L
则有：AB=AC,BD=BC,BD垂直于AB
又AM+AN=2AC,AN=AB+ BN
BN=MC
在三角形MKC和NLB中,BN=MC,角LBN
=ABC=MCK
两三角形全等,MK=NL
在三角形NEL和MEK中,MK=NL,对角相等,两个三角形全等,ME=NE
在直角三角形DCM和DBN中,BD=BC,BN=MC
两个三角形全等
DM=DN
则：E为等腰三角形DMN中线,故：DE垂直MN

　　证明:过N做NF⊥x轴于F
　　∵NF⊥x轴 MK⊥BC
　　∴∠NFC=∠MKF=90°
　　∵AB=AC
　　∴∠ABC=∠MCK
　　∵∠NBF=∠ABC
　　∴∠NBF=∠MCK
　　在△BFN和△MCK中
　　∠NFC=∠MKF=90°
　　∠FBN=∠MCK
　　BN=CM
　　∴△BFN≌△M...

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　　证明:过N做NF⊥x轴于F
　　∵NF⊥x轴 MK⊥BC
　　∴∠NFC=∠MKF=90°
　　∵AB=AC
　　∴∠ABC=∠MCK
　　∵∠NBF=∠ABC
　　∴∠NBF=∠MCK
　　在△BFN和△MCK中
　　∠NFC=∠MKF=90°
　　∠FBN=∠MCK
　　BN=CM
　　∴△BFN≌△MCK(AAS)
　　∴NF=MK
　　在△EFN和△MEK中
　　∠BEN=∠MEK
　　∠NFC=∠MKF
　　NF=MK
　　∴△EFN≌△MEK(AAS)
　　∴EN=ME
　　连接BD,MD,DN
　　∵CD⊥AC
　　∴∠DCA=90°
　　∵BD⊥AN
　　∴∠DBN=90°
　　在△BND和△MCD中
　　BN=CM
　　∠NBD=∠MCD=90°
　　BD=CD
　　∴△BND≌△MCD(SAS)
　　∴DN=DM
　　∵NE=ME
　　∴DE⊥MN
　　∵△ENF≌△MEK
　　∴EF=EK
　　∵△BFN≌△MKC
　　∴BF=CK
　　∴EK=EF=1/2FK
　　=1/2(BF+OB+OC-CK)
　　=1/2(OB+OC)
　　∴EK/BC=1/2

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证明:过N做NF⊥x轴于F
∵NF⊥x轴 MK⊥BC
∴∠NFC=∠MKF=90°
∵AB=AC
∴∠ABC=∠MCK
∵∠NBF=∠ABC
∴∠NBF=∠MCK
在△BFN和△MCK中
∠NFC=∠MKF=90°
∠FBN=∠MCK
BN=CM
∴△BFN≌△MCK(AAS)
∴NF=MK
在...

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证明:过N做NF⊥x轴于F
∵NF⊥x轴 MK⊥BC
∴∠NFC=∠MKF=90°
∵AB=AC
∴∠ABC=∠MCK
∵∠NBF=∠ABC
∴∠NBF=∠MCK
在△BFN和△MCK中
∠NFC=∠MKF=90°
∠FBN=∠MCK
BN=CM
∴△BFN≌△MCK(AAS)
∴NF=MK
在△EFN和△MEK中
∠BEN=∠MEK
∠NFC=∠MKF
NF=MK
∴△EFN≌△MEK(AAS)
∴EN=ME
连接BD,MD,DN
∵CD⊥AC
∴∠DCA=90°
∵BD⊥AN
∴∠DBN=90°
在△BND和△MCD中
BN=CM
∠NBD=∠MCD=90°
BD=CD
∴△BND≌△MCD(SAS)
∴DN=DM
∵NE=ME
∴DE⊥MN
∵△ENF≌△MEK
∴EF=EK
∵△BFN≌△MKC
∴BF=CK
∴EK=EF=1/2FK
=1/2(BF+OB+OC-CK)
=1/2(OB+OC)
∴EK/BC=1/2

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