Question

如图,已知AC=CD=DB,BM=2BN,AM=MC,如果MN=5cm,求AB、CN的长.

Answer 1

∵AC=CD=DB,BM=2BN,AM=MC

∴BN=MN=BD+DN=(1/3)AB+DN=5;

∵MN=CD-DN+CM=(1/3)AB-DN+CM=5;

∵AM=AC-MC=(1/3)AB-MC

∴MC=(1/6)AB;

∴BM=BN+NM=(2/3)AB+CM=10;

∴AB=12;

∴ND=BN-(1/3)AB=5-4=1;

∴CN=CD-ND=(1/3)AB-ND=4-1=3;