27.如圖,⊙O是等邊三角形ABC的外接圓,過(guò)點(diǎn)A作AB的垂線交⊙O于點(diǎn)H.
(1)若點(diǎn)G是劣弧BC上一點(diǎn)(不與點(diǎn)B、C重合),直線GC、AH交于點(diǎn)D,連接GA,GB.求證:GA平分∠BGD;
(2)在(1)條件下,將AD繞點(diǎn)A順時(shí)針旋轉(zhuǎn)60°得到線段AF.
①若CG>BG,求證:點(diǎn)F落在射線BG上;
②若FB=
FG,求線段AB與線段AD的數(shù)量關(guān)系.