Question

如图 ,△ABC中,∠ACB=90°,CD⊥AB

Answer 1

证明：因为FM//AB,所以△CFM∽△CDB,则MB/CM=FD/CF,即MB/FD=CM/CF①

由于CD⊥AB,所以∠CFM=∠ADC=90°,且∠FCM=∠DAC,因此△CFM∽△ADC,

则CM/AC=CF/AD,即CM/CF=AC/AD②,因为AE为∠BAC平分线,所以∠CAE=∠DAF,且∠ACE=∠ADF,于是△ACE∽△ADF,因此AC/AD=CE/FD③,①、②、③联立可得CE/FD=MB/FD,即CE=MB.