如图,三角形ABC内接于圆O

Question

如图,三角形ABC内接于圆O
 

Answer 1

1,  AB=BC,  ∠BAC=∠BCF 又∠BAC=∠BDC

    故 ∠BCF=∠BDC  又∠FBC=∠CBD

故△FBC∽△CBD 

故∠BFC=∠BCD  又BD=BC  ∠FBC=∠BCD

故∠BFC=∠FBC, 故BC=CF

2, AB=BC ∠FAB=∠ACB, 又∠ACB=∠ADB

   ∠FAB=∠ADB  ∠FBA=∠ABD

△FAB∽△ADB  ∠BAC=∠ADB   cos(ADB)=3/4

DB/AB=AB/BF  AB^2=DB*BF=DB*(DB-DF)

∠BFC=∠FBC ∠DAF=∠FBC ∠BFC=∠AFD

∠DAF=∠AFD  DA=DF

AB^2=DB*(DB-DA)=DB^2-DB*DA

AB^2=DA^2+DB^2-2DA*DB*cos(ADB)

DB^2-DB*DA=DA^2+DB^2-3DA*DB/2

DA^2-DA*DB/2=0

DA=DB/2

DA/DB=1/2