题目如图,⊙O⊙O⊙O是△ABC\triangle ABC△ABC的外接圆,ABABAB为⊙O⊙O⊙O的直径,点EEE为⊙O⊙O⊙O上一点,EF/ /ACEF/\!/ACEF//AC交ABABAB的延长线于点FFF,CECECE与ABABAB交于点DDD,连接BEBEBE,若∠BCE=12∠ABC.∠BCE=\dfrac{1}{2}∠ABC.∠BCE=21∠ABC.(1)(1)(1)求证:EFEFEF是⊙O⊙O⊙O的切线.(2)(2)(2)若BF=2BF=2BF=2,sin∠BEC=35\sin∠BEC=\dfrac{3}{5}sin∠BEC=53,求⊙O⊙O⊙O的半径.知识点:切线的判定与性质章节:图形的性质 / 圆