等边三角形ABC外接于圆O,D为弧BC上一点（劣弧）,AC,BD延长线交于点E,连接AC,做CF‖AD交圆0于F,连接BF交AD于点G

1. 三角形GBD是等边三角形
2.
考虑三角形ABG和EBC
角ABG=角EBC
角AGB=角ECB = 120度
三角形ABG和EBC相似
AB/BE = BG/BC
AB*BC = BE *BG
AB = BC =√5
BE = BD + DE = BG + 2
BG (BG+2) = 5
BG = √6-1
DG =BG = √6-1