Question

AB是圆O的直径,EF是弦,作AC垂直EF BD垂直EF AC交圆O与G

Answer 1

1、CE=DF成立.作OG//AC,则OG⊥CD.O是AB的中点.G是直角梯形CD边的中点,CG=DG连接OE、OF,OE=OF.===>EG=FGCE=CG-EG=DG-GF=DF2、结论依然成立EF是平移得到,设BC1//EF,BC1CD是矩形作OG1⊥CD于G1,OH⊥BC1,OH垂直平分BC1故,OG1垂直平分CD,G1C=G1D又,等腰三角形OEF,OE=OF,===>EG1=G1F所以,CE=DF3、EF=0,E、F重合,CE=CF=DF=DE4、AB是直径,AE⊥BE RtΔACE∽RtΔBDEAC:CE=DE:BDAC×BD=CE×ED=(CD/2)^24AC×BD=CD^2