Question

在Rt三角形ABC中,∠ACB=90°,CD⊥AB于点D,AE平分∠CAB于点F,交BC于点E,FN∥AB交BC于N,下

Answer 1

∠ACB=90°,设BC=a,CA=b,则AB=c=√(a^2+b^2),

CD⊥AB,∴CD=ab/c,AD=b^2/c,

AE平分∠CAB,∴CE/EB=AC/AB=b/c,∴CE=ab/(b+c),同理,CF/FD=AC/AD=c/b,

FN∥AB,∴CN/NB=CF/FD=c/b,∴BN=ab/(b+c)=CE,②正确,弃C.

CF=c*CD/(b+c)=ab/(b+c),EN=a-2ab/(b+c)=a(c-b)/(b+c),

∴CF=EN,b=c-b,c=2b,①错,弃B,D,选A.