3.
\((\)本小题满分\(10\)分\()\)
已知:\(AB\)为\(⊙O\)的直径,\(C\)是\(⊙O\)上一点,如图,\(AB=12\),\(BC=4\sqrt{3}.BH\)与\(⊙O\)相切于点\(B\),过点\(C\)作\(BH\)的平行线交\(AB\)于点\(E\).
\((1)\)求\(CE\)的长;
\((2)\)延长\(CE\)到\(F\),使\(EF=\sqrt{2}\),连接\(BF\)并
延长\(BF\)交\(⊙O\)于点\(G\),求\(BG\)的长;
\((3)\)在\((2)\)的条件下,连接\(GC\)并延长
\(GC\)交\(BH\)于点\(D\),求证:\(BD=BG\)