题目

如图. 为半圆 的直径，点 为半圆 上一点，过点 作半圆 的切线 交 的延长线于点 .过点 作 于点 ，交半圆 于点 ，过点 作 于点 ，连接 ， ， . （1） 求证： ； （2） 填空：①连接 ，当 的度数为时，四边形 为菱形； ②若 . ，则 的长为. 答案：证明：如图1，连接 OC .∵ CD 是半圆 O 的切线， ∴ OC⊥DE . 又∵ AE⊥CD ， ∴ OC//AE . ∴ ∠EAC=∠ACO . ∵ OA=OC ， ∴ ∠BAC=∠ACO . ∴ ∠EAC=∠BAC . ∵ AE⊥CD ， CF⊥AB ， ∴ ∠AEC=∠AFC=90° . ∵ AC=AC ， ∴ △ACE≌△ACF(AAS) . 【1】30º【2】94On a cold December morning, my mother and I were walking home from a pizza store. We were dressed warmly and equipped  36  the video we had been dying to watch. I was feeling a little  37 , as I was carrying our shopping, bags of snacks and the video.  They were so heavy that I decided to  38  some things. So I started to walk towards the garbage can when I  39  a poor man walking his bike out of the restaurant in front of us. He held a paper bag with his dirty hand. He  40  over to another nearby garbage can and started  41  it.  I suddenly felt very  42 . I knew this man would take all he could get,  43  I walked up to him and  44  the drink and some snacks over to him. The man, with lines on his face and wrinkles on his forehead, looked up in  45  and took what I gave him. A huge smile  46  across his face and this caused me to feel indescribable  47 . I felt like I couldn’t be  48  with myself, but then he said: “Wow, first someone gives me this sandwich, then this drink, and now some  49  food; this is my daughter’s  50  day!” He thanked me  51  and started off on his bike. I even heard him whistling a song as he rode away.  I now  52  what is meant by the saying “giving is getting”. Everyone in the world needs help, everyone can  53  help and everyone will be helped by showing  54 .  The image of that man’s happiness caused by my small gift appears in my mind every time I have the  55  to do something nice.  36. A. forB. ofC. withD. about 37. A. excitedB. puzzledC. tiredD. satisfied 38. A. pick outB. eat upC. put downD. throw away 39. A. heardB. noticedC. feltD. watched 40. A. headedB. rodeC. ranD. fled 41. A. breaking intoB. looking throughC. staring atD. searching for 42. A. coldB. afraidC. guiltyD. content 43. A. butB. becauseC. soD. if 44. A. turnedB. thoughtC. tookD. handed 45. A. surpriseB. detailC. caseD. return 46. A. disappearedB. pausedC. existedD. spread 47. A. disappointmentB. shameC. satisfactionD. victory 48. A. sadderB. angrierC. happierD. crazier 49. A. cheapB. tastyC. cleanD. useful 50. A. luckyB. busyC. interestingD. quiet 51. A. carefullyB. happilyC. calmlyD. fortunately 52. A. rememberB. understandC. appreciateD. recognize 53. A. refuseB. receiveC. offerD. find 54. A. kindnessB. eagernessC. willingnessD. braveness 55. A. chanceB. desireC. purposeD. feeling