题目如图,△AOB\triangle AOB△AOB以OOO为圆心,OBOBOB为半径的圆交OAOAOA于点CCC,连接BCBCBC,过点OOO作OD/ /BCOD/\!/BCOD//BC交ABABAB延长线于点DDD,∠AOB=2∠ABC.∠AOB=2∠ABC.∠AOB=2∠ABC.(1)(1)(1)求证:ABABAB是⊙O⊙O⊙O的切线;(2)(2)(2)若AB=4AB=4AB=4,tan∠BCO=2\tan∠BCO=2tan∠BCO=2,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