圆O是等腰三角形ABC的外接圆,AB=AC,延长BC到点D,使CD=AC,连接AD交圆O于点E连接BE交AC于点F,若AE=6,BE=8,求EF的长
问题描述:
圆O是等腰三角形ABC的外接圆,AB=AC,延长BC到点D,使CD=AC,连接AD交圆O于点E连接BE交AC于点F,若AE=6,BE=8,求EF的长
答
∵AC=CD,∴∠CAD=∠D∴∠ACB=∠CAD+∠D=2∠CAD∵∠CAD=∠EBC,∴∠ACB=2∠EBC∵AB=AC∴∠ABC=∠ACB=2∠EBC∴∠ABE=∠CBE∴BE平分∠ABE∵∠EAC=∠EBC=∠ABE,∠AEF=∠BEA∴△AEF∽△BEA∴AE:BE=EF:AE,...