如图,圆O是三角形ABC的外接圆。角BAC的平分线交圆O于点D,角ABC的平分...答:∴∠BAD=∠CAD,而弧CD所对圆周角是∠CAD,∠CBD,∴∠CAD=∠CBD,同理,∠BAD=∠BCD,∴∠CBD=∠BCD,∴BD=CD,又∵∠DBI=∠DBC+∠CBI=∠CAD+∠ABC/2,∠BID=∠BAI+∠ABI=∠CAD+∠ABC/2,∴∠DBI=∠BID,∴BD=DC=DI ∠BAC=120°,∴∠BDC=180°-120°= 60°,而△BDC是圆内接等边三角...
如图,圆o是△ABC的外接圆,AD平分∠BAC,交圆o于点D,弦DE∥BA,交AC于点...答:OF垂直平分AD 证明:∵AB∥DE,∴∠BAD=∠ADE ∵AD平分∠BAC,∴∠BAD=∠CAD ∴∠CAD=∠ADE,∴AF=DF 连接OA,OD,则OA=OD ∵OF=OF,∴△AOF≌△DOF(SSS)由图像可知△AOF和△DOF关於直线OF对称 由对称的性质可知OF垂直平分AD