如图,在Rt三角形ABC中,角C=90度,AE平分角BAC交BC于E,点O在AB上,以OA为半径的圆,交AC于D,交AC于G,且点E在圆O上,连结DE,BF切圆O于点F.(1)求证:BE=BF;(2)若角EBF=60度,BF=2,求DE的长及角AEC的度数.
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![如图,在Rt三角形ABC中,角C=90度,AE平分角BAC交BC于E,点O在AB上,以OA为半径的圆,交AC于D,交AC于G,且点E在圆O上,连结DE,BF切圆O于点F.(1)求证:BE=BF;(2)若角EBF=60度,BF=2,求DE的长及角AEC的度数.](/uploads/image/z/1601777-65-7.jpg?t=%E5%A6%82%E5%9B%BE%2C%E5%9C%A8Rt%E4%B8%89%E8%A7%92%E5%BD%A2ABC%E4%B8%AD%2C%E8%A7%92C%3D90%E5%BA%A6%2CAE%E5%B9%B3%E5%88%86%E8%A7%92BAC%E4%BA%A4BC%E4%BA%8EE%2C%E7%82%B9O%E5%9C%A8AB%E4%B8%8A%2C%E4%BB%A5OA%E4%B8%BA%E5%8D%8A%E5%BE%84%E7%9A%84%E5%9C%86%2C%E4%BA%A4AC%E4%BA%8ED%2C%E4%BA%A4AC%E4%BA%8EG%2C%E4%B8%94%E7%82%B9E%E5%9C%A8%E5%9C%86O%E4%B8%8A%2C%E8%BF%9E%E7%BB%93DE%2CBF%E5%88%87%E5%9C%86O%E4%BA%8E%E7%82%B9F.%EF%BC%881%EF%BC%89%E6%B1%82%E8%AF%81%EF%BC%9ABE%3DBF%EF%BC%9B%EF%BC%882%EF%BC%89%E8%8B%A5%E8%A7%92EBF%3D60%E5%BA%A6%2CBF%3D2%2C%E6%B1%82DE%E7%9A%84%E9%95%BF%E5%8F%8A%E8%A7%92AEC%E7%9A%84%E5%BA%A6%E6%95%B0.)
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