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            • 1. 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:\(BD=BG\).
            • 2. 在菱形\(ABCD\)中,对角线\({AC}{,}{BD}\)交于点\(O{,}E\)为\(AC\)上点,且\(CE{=}CB{,}F\)为\(BE\)上点,\(M\)为\(BC\)上点,且\(MF{⊥}BE\),并与\(OB\)相交于点\(N\).
              \((1)\)求证:\({\triangle }BOE\)∽\({\triangle }MFB\);
              \((2)\)若\(BD{=}\dfrac{2}{3}{AC}{,}BF{=}a\),求\(MN\)的长\({.}(\)结果用\(a\)表示\()\)
            • 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:\(BD=BG\)

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