如图△ABC中,∠ACB=90°,CD为AB边上的高,DE⊥AC于E,△ADE的中线AG的延长线交BC于F.(1)求证:F是BC中点;(2)若CF=FG,求证:FG=1/3AF;(3)在(2)的条件下,若AC=6√2,求DE的长.
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![如图△ABC中,∠ACB=90°,CD为AB边上的高,DE⊥AC于E,△ADE的中线AG的延长线交BC于F.(1)求证:F是BC中点;(2)若CF=FG,求证:FG=1/3AF;(3)在(2)的条件下,若AC=6√2,求DE的长.](/uploads/image/z/4327756-52-6.jpg?t=%E5%A6%82%E5%9B%BE%E2%96%B3ABC%E4%B8%AD%2C%E2%88%A0ACB%3D90%C2%B0%2CCD%E4%B8%BAAB%E8%BE%B9%E4%B8%8A%E7%9A%84%E9%AB%98%2CDE%E2%8A%A5AC%E4%BA%8EE%2C%E2%96%B3ADE%E7%9A%84%E4%B8%AD%E7%BA%BFAG%E7%9A%84%E5%BB%B6%E9%95%BF%E7%BA%BF%E4%BA%A4BC%E4%BA%8EF.%EF%BC%881%EF%BC%89%E6%B1%82%E8%AF%81%EF%BC%9AF%E6%98%AFBC%E4%B8%AD%E7%82%B9%EF%BC%9B%EF%BC%882%EF%BC%89%E8%8B%A5CF%3DFG%2C%E6%B1%82%E8%AF%81%EF%BC%9AFG%3D1%2F3AF%EF%BC%9B%EF%BC%883%EF%BC%89%E5%9C%A8%EF%BC%882%EF%BC%89%E7%9A%84%E6%9D%A1%E4%BB%B6%E4%B8%8B%2C%E8%8B%A5AC%3D6%E2%88%9A2%2C%E6%B1%82DE%E7%9A%84%E9%95%BF.)
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