如图，⊙O的半径OD，OE分别垂直于弦AB和AC，连结DE交AB，AC于F，G。求证：⑴AF^2=AB^2（已证出）⑵AG^2=DF·GE
热心网友
解: ∵OD⊥AB OE⊥AC ∴AD⌒=DB⌒ AE⌒=EC⌒ (AB⌒表示AB劣弧) ∴∠AFG=1/2×(DB⌒+AE⌒) ∠AGF=1/2×(AD⌒+EC⌒) ∴∠AFG∠AGF ∴AG=AF连AD,AE ∠DAF= 1/2×(DB⌒) ∠AEG= 1/2×(AD⌒) ∴∠DAF＝∠AEG ∠ADF= 1/2×(AE⌒) ∠EAG= 1/2×(EC⌒) ∴∠ADF＝∠EAC ∴△ADF∽△AEG ∴AF/GE=DF/AG AG×AF=DF×GE既AG^2=DF·GE