题目

如图，AB为⊙O的直径，AD平分∠BAC交⊙O于点D，DE⊥AC交AC的延长线于点E，FB是⊙O的切线交AD的延长线于点F.1.求证：DE是⊙O的切线2.若DE=3，⊙O的半径为5，求BF的长  答案： 1.证明:如图(1)连接OD. ∵AD平分∠BAC， ∴∠1=∠2.又∵OA=OD ，∴∠1=∠3.∴∠2=∠3. ∴OD∥AE. ∵DE⊥AE，∴DE⊥OD. 而D在⊙O上，∴DE是⊙O的切线.2.BF=解析: (2)过D作DG⊥AB 于G. ∵DE⊥AE ，∠1=∠2.∴DG=DE=3 ，半径OD=5.在Rt△ODG中，根据勾股定理: OG＝＝＝4，∴AG=AO+OG=5+4=9.∵FB是⊙O的切线， AB是直径，∴FB⊥AB.而DG⊥AB The words, _______ steal vegetables (偷菜)，60th anniversary (60周年), humble abode (蜗居), have been on the list of 2009’s 10 news keywords made by Xinhua News Agency. A. that is B. besides       C. including    D. included