题目

如图，已知AB是⊙O的直径，直线CD与⊙O相切于点C，AC平分∠DAB． （1）求证：AD⊥DC； （2）若AD=2，AC=，求AB的长． 答案：  考点： 切线的性质；相似三角形的判定与性质．  专题： 综合题；压轴题． 分析： （1）连接OC，根据切线的性质得到OC与CD垂直，进而得到∠OCA+∠DCA=90°，由AC为角平分线，根据角平分线定义得到两个角相等，又OA=OC，根据等边对等角得到又得到另两个角相等，等量代换后得到∠DAC=∠OCA，根据等角 There’s a man in the habit of hitting me on the head with an umbrella. At first I couldn’t stand it, now I’m used to it. I don’t know his name. I know he’s average in appearance, wears a gray suit, and has a common face. I met him five years ago one hot morning when I was sitting on a tree-shaded bench in Palermo Park, reading the paper. Suddenly I felt something touch my head. It was the very same man who now, as I’m writing, keeps hitting me, mechanically (机械地) and impassively, with an umbrella. On that occasion I turned around filled with anger. He just kept on hitting me. I asked him if he was crazy, he didn’t even seem to hear me. Then I threatened to call a policeman. Calmly, cool as a cucumber, he stuck with his task. After a few moments of hesitation, and seeing that he was not about to change his attitude, I stood up and hit him on the nose. The man fell down, but he immediately got back on his feet, obviously with great effort, and without a word again began hitting me on the head with the umbrella. His nose was bleeding and, at that moment, I felt sorry for him. I felt regret for having hit him so hard. After all, the man wasn’t exactly hitting me; he was merely tapping me lightly with his umbrella, not causing any pain at all. Of course, those taps were extremely bothersome. As we all know, when a fly lands on your forehead, you don’t feel any pain; what you feel is annoyance. Well then, that umbrella was one huge fly that kept landing on my head time after time. Convinced that I was dealing with a madman, I tried to escape. But the man followed me, wordlessly continuing to hit me. So I began to run (I should point out that not many people run as fast as I do). He took off after me, trying to land a blow. The man was out of breath so that I thought, if I continued to force him to run at that speed, he would drop dead right then and there.  1.When the man began to strike the author with an umbrella, the author ________.    A. became angry    B. called the police    C. turned around and escaped    D. turned around and fought back 2.The author would most probably agree that the man was ________.    A. deaf          B. blind           C. dead           D. mad 3.The author felt sorry for the man because ________.    A. the man formed a bad habit of beating others    B. he hit the man so hard that his nose bled    C. the man couldn’t catch up with him    D. there was a fly on the man’s head 4.It can be learned from the passage that the man ________.    A. shouted loudly while hitting the author    B. wanted to tell the author something    C. ran after the author breathlessly    D. acted as if he were a fly