lesson 10

10

Text A The Telephone

When I was growing up in Magdaluna, a small Lebanese village in the terraced, rocky mountains east of Sidon, time didn't mean much to anybody, except maybe to those who were dying. In those days, there was no real need for a calendar or a watch to keep track of the hours, days, mouths, and years. We knew what to do and when to do it, just as the Iraqi geese knew when to fly north, driven by the hot wind that blew in from the desert. The only timepiece we had need of then was the sun. It rose and set, and the seasons rolled by and we sowed seed and harvested and ate and played and married our cousins and had babies who got whooping cough and chickenpox—and those children who survived grew up and married their cousins and had babies who got whooping cough and chickenpox. We lived and loved and toiled and died without ever needing to know what year it was, or even the time of day.

It wasn't that we had no system for keeping track of time and of the important events in our lives. But ours was a natural or, rather, a divine calendar, because it was framed by acts of God: earthquakes and droughts and floods and locusts and pestilences. Simple as our calendar was, it worked just fine for us.

Take, for example, the birth date of Teta Im Khalil, the oldest woman in Magdaluna and all the surrounding villages. When I asked Grandma, "How old is Teta Im Khalil?"

Grandma had to think for a moment; then she said, "I've been told that Teta was born shortly after the big snow that caused the roof on the mayor's house to cave in."

"And when was that?" I asked.

"Oh, about the time we had the big earthquake that cracked the wall in the east room."

Well, that was enough for me. Y ou couldn't be more accurate than that, now, could you?

And that's the way it was in your little village for as far back as anybody could remember. One of the most unusual of the dates was when a whirlwind struck during which fish and oranges fell from the sky. Incredible as it may sound, the story of the fish and oranges was true, because men who would not lie even to save their own souls told and retold that story until it was incorporated into Magdaluna's calendar.

The year of the fish-bearing whirlwind was not the last remarkable year. Many others followed in which strange and wonderful things happened. There was, for instance, the year of the drought, when the heavens were shut for months and the spring from which the entire village got its drinking water slowed to a trickle. The spring was about a mile from the village, in a ravine that opened at one end into a small, flat clearing covered with fine gray dust and hard, marble-sized goat droppings. In the year of the drought, that little clearing was always packed full of noisy kids with big brown eyes and sticky hands, and their mothers—sinewy, oberworked young women

with cracked, brown heels. The children ran around playinh tag or hide-and-seek while the women taked, shooed flied, and awaited their turns to fill up their jars with drinking water to bring home to their napping men and wet babies. There were days when we had to wait from sunup until late afternoon just to fill a small clay jar with precious, cool water.

Sometimes, amid the long wait and the heat and the flies and the smell of goat dung, tempers flared, and the young women, anxious about their babies, argued over whose turn it was to fill up her jar. And sometimes the arguments escalated into full-blown, knockdown-dragout fights; the women would grab each other by the hair and curse and scream and spit and call each other names that made my ears tingle. We little brown boys who went with our mothers to fetch water loved these fights, because we got to see the women’s legs and their colored panties as they grappled and rolled around in the dust. Once in a while, we got lucky and saw much more, because some of the women wore nothing at all under their long dresses. God, how I used to look forward to those fights. I remember the rush, the excitement, the sun dancing on the dust clouds as a dress ripped and a young white breast was revealed, then quickly hidden. In my calendar, that year of drought will always be one of the best years of my childhood.

But, in another way, the year of the drought was also one of the worst of my life, because that was the year that Abu Raja, the retired cook, decided it was time Magdaluna got its own telephone. Every civilized village needed a telephone, he said, and Magdaluna was not going to get anywhere until it had one. A telephone would link us with the outside world. A few men —like the retired Turkish-army drill sergeant, and the vineyard keeper—did all they could to talk Abu Raja out of having a telephone brought to the village. But they were outshouted and ignored and finally shunned by the other villagers for resisting progress and trying to keep a good thing from coming to Magdaluna.

One warm day in early fall, many of the villagers were out in their fields repairing walls or gathering wood for the winter when the shout went out that the telephone-company truck had arrived at Abu Raja’s dikkan, or country store. When the truck came into view, everybody dropped what they were doing and ran to Abu Raja’s house to see what was happening.

It did not take long for the whole village to assemble at Abu Raja’s dikkan. Some of the rich villagers walked right into the store and stood at the elbows of the two important-looking men from the telephone company, who proceeded with utmost gravity, like priests at Communion, to wire up the telephone. The poorer villagers stood outside and listened carefully to the details relayed to them by the not-so-poor people who stood in the doorway and could see inside.

“The bald man is cutting the blue wire, “someone said.

“He is sticking the wire into the hole in the bottom of the black box,”someone else added.

“The telephone man with the mustache is connecting to pieces of wire. Now he is twisting the ends together, ”a third voice chimed in.

Because I was small, I wriggled my way through the dense forest of legs to get a firsthand look at the action. Breathless, I watched s the men in blue put together a black machine that supposedly would make it possible to talk with uncles, aunts, and cousins who lived more than two days’ride away.

It was shortly after sunset when the man with the mustache announced that the telephone was ready to use. He explained that all Abu Raja had to do was lift the receiver, turn the crank on the black box a few times, and wait for an operator to take his call. Abu Raja grabbed the receiver and turned the crank forcefully. Within moments, he was talking with his brother in Beirut. He didn’t even have to raise his voice or shout to be heard.

And the telephone, as it turned out, as bad news. With its coming, the face of the village began to charge. One of the first effects was the shifting of the village’s center. Before the telephone’s arrival, the men of the village used to gather regularly at the house of Im Kaleem, a short, middle-aged widow with jet-black hair and a raspy voice that could be hard all over the village, even when she was only whispering. She was a devout Catholic and also the village whore. The men met at her house to argue about politics and drink coffee and play cards or backgammon. Im Kaleem was not a true prostitute, however, because she did not charge for their services—not even for the coffee and tea that she served the men. She did not need the money; her son, who was overseas in Africa, send her money regularly. Im Kaleem loved all the men she entertained, and they loved her, every one of them .in a way, she was married to all the men in the village. Everybody knew it but nobody objected. Actually I suspect the women did not mind their husbands’visits to Im Kaleem. Oh, they wrung their hands and complained to one another about their men’s unfaithfulness, but secretly they were relieved, because Im Kaleem took some of the pressure off them and kept the men out of their hair while they attended to their endless chores. Im Kaleem was also a kind of confessor and troubleshooter, talking sense to those men who were having family problems, especially the younger ones.

Before the telephone came to Magdaluna, Im Kaleems house was bustling at just about any time of day, especially at night, when the loud voices of the men talking, laughing, and arguing could be heard in the street below—a reassuring, homey sound. Her house was an island of comfort, an oasis for the weary village men, exhausted from having so little to do.

But it wasn’t long before many of those men—younger ones especially —started spending more of their days and evenings at Abu Raja’s dikkan. There, they would eat and drink and talk and play checkers and backgammon, and then lean their chairs back against the wall—the signal that they were ready to toss back and forth, like a ball, the latest rumors going around the village. And they were always looking up from their games and drinks and talk t glance at the phone in the corner, as if expecting it to ring any minute and bring news that would change their lives and deliver them from their aimless existence. In the meantime, they smoked cheap, hand-rolled cigarettes, dug dirt out from under their fingernails with big pocketknives, and drank lukewarm sodas that they called Kacula, Seffen-Ub, and Bebsi.

The telephone was also bad news for me personally. It took away my lucrative business—a source

of much-needed income. Before, I used to hang around Im Kaleem’s courtyard and play marbles with the other kids, waiting for some man to call down from a window and ask me to run to the store for cigarettes or liquor, or to deliver a message to his wife, such as what he wanted for supper. There was always something in it for me: a ten- or even a twenty-five-piaster piece. On a good day, I ran nine or ten of those errands, which assured a steady supply of marbles that I usually lost to other boys. But as the days went by fewer and fewer men came to Im Kaleem’s, and more and more congregated at Abu Raja’s to wait by the telephone. In the evenings, the laughter and noise of the men trailed off and finally stopped.

At Abu Raja’s dikkan, the calls did eventually come, as expected, and men and women started leaving the village the way a hailstorm begins: first one, then two, then bunches. The army took them.

Jobs in the cities lured them. And ships and airplanes carried them to such faraway places as Australia and Brazil and New Zealand My friend Kameel, his cousin Habeeb, and their cousins and my cousins all went away to become ditch diggers and mechanics and butcher-shop boys and deli owners who wore dirty aprons sixteen hours a day, all looking for a better life than the one they had left behind. Within a year, only the sick, the old, and the maimed were left in the village. Magdaluna became a skeleton of its former self, desolate and forsaken, like the tombs, a place to get away from.

Finally, the telephone took my family away, too. My father got a call from an old army buddy who told him that an oil company in southern Lebanon was hiring interpreters and instructors. My father applied for a job and got it, and we moved to Sidon, where I went to a Presbyterian missionary school and graduated in 1962. Three years later, having won a scholarship, I left Lebanon for the United States. Like the others who left Magdaluna before me, I am still looking for that better life.

典范英语Lesson10

++++++ Lesson 8 The Golden Touch The children were dipping strawberries into chocolate. “They look yummy!”said Chip. “They taste yummy!”said Kippper. Kipper went to Biff’s room.He had chocolate on his hands.He got chocolate on everything he touched. “Go away,Kipper!”said Biff. “You’re getting chocolate on everything,”said Chip. “I wish everything I touched turned into chocolate,”said Kipper. “That’s just greedy,’said Chip. Just then the magic key began to glow.It took the children into an adventure. They saw a girl sitting by a river.She was crying. “What’s the matter?”asked Biff. “Come with me and I’ll show you,”said the girl.”My name is Zoe.”Zoe took them to a palace. The children gasped.The palace was made of gold,and a gold tree stood outside. Zoe took the children inside.Everything was made of gold,even the food on the table! “My father is King Midas,”said Zoe sadly.”He made a wish that everything he touched turned intyo gold.Now his wish has come true!”

高二年段实验班“培优”工作方案

高二年段上学期工作要点 年段现状：经过高一年全体师生的共同努力，年段常规管理制度已基本形成，学生行为习惯得到较为改善。但相当一部分学生良好的学习习惯仍没有养成，学习方式、学习的主动性和积极性等都有待进一步改善和提高。同时，年段教师的积极性也有待激发，如何让科任教师更好地融入年段管理当中更是一个亟待解决的难题。 鉴以此，年段本学期的工作除了继续抓好学生的常规教育工作，将把工作的重心更多地转移到年段教学工作和学生成绩的提高上。具体设想如下： 第一，充分利用班会课、学生集会等活动，加强学生的理想激励教育，标高定位，激发学生学习的自信心、主动性和积极性。 第二，切实做好文理科学生学习方法的指导，努力引导学生转变学习方式，培养学生自主学习的习惯和能力。 第三，加强师生间的交流和沟通，通过落实导师制、设立班级教学意见箱等方式，及时了解学生学习动态，增强师生情感交流。 第四，抓早抓实“尖子生”的培养工作，通过对尖子生的精细分析，理想激励、立体爱护、家长配合等措施，让尖子生的潜力得到最大的发挥。 第五，通过制定班级评优评先评分细则、建立班主任出勤登记、通报制度，进一步加强对班主任工作的管理，增强班主任工作的实效性。 第六，开展以宿舍为单位的舍标设计、宿舍生活摄影展、接力赛等“宿舍文体活动节”，培养舍员间“比、赶、超”的竞争意识，营造竞争、团结、和谐的宿舍环境。 第七，努力动员特长生向体育、艺术方向发展，为以后包括这些专业打下良好的基础。

高二年段实验班“培优”工作方案（讨论稿）一、确定名单、组织动员：（第3周） 培优对象：总成绩位居年段、实验班前列且单科成绩较为突出的学生。精细分析、精准确认、适当调整。原则上每班5人。 二、培优科目：语、数、英、物、化、生六科高考科目；每科学生10人左右；每周二科，以此轮流。 三、时间地点：本学期共安排三轮培优，具体为每周二、四晚自修第三节课（20:45——21:30）地点：二楼年段室 第一轮（第4、6、7、8、9、10周）； 第二轮（第12、13、14、15、16、17周）； 第三轮（第18、19、20、21、22、23周）。 四、具体要求： 1、年段统一制定“培优”课程表，科任教师严格按照课程表安排上课； 2、“培优”方式，主要以试卷讲评为主，可依托试卷讲解，分题型、专题等内容进行授课，注重学生归纳总结能力、自主拓展能力的培养，力求本学期学生在学科素养、成绩有一个质的提高。 3、授课教师须提前一周命好试卷并分发给学生完成，试题以“精、少”为主，可适当加大难度。 五、课程安排： 第4周：周二周四第6周：周二周四 第7周：周二周四第8周：周二周四 第9周：周二周四第10周：周二周四

三角函数题型总结-教师版

三角函数题型总结-教师版

111111 cos sin sin 2224 S x y = =?=ααα， …… …………7分 2221112||[cos()]sin()sin(2)223343 S x y πππ = =-+?+=-+ααα． … …………9分 依题意得 2sin 22sin(2)3π=-+αα， 整 理得 cos20 =α． ………………11分 因为 62 ππ<<α， 所以 23π <<πα， 所 以 22 π= α， 即 4 π = α． …… …………13分 2、三角形中求值 〖例〗（2013年高考北京卷（理））在△ABC 中,a =3,b 6,∠B =2∠A . (I)求cosA 的值; (II)求c 的值. 【答案】 解:(I)因为a =3,b =2 ,∠B =2∠A . 所以在△ABC

中,由正弦定理得3sin sin 2A A =.所以2sin cos sin 3A A A =.故cos 3 A =. (II)由(I)知 cos A = ,所以 sin A == .又因为 ∠B=2∠A,所以2 1cos 2cos 13 B A =-= .所以2sin 1cos B B = -= . 在△ABC 中,53sin sin()sin cos cos sin C A B A B A B =+=+=所以sin 5sin a C c A ==. 【举一反三】 （2013年普通高等学校招生统一考试大纲版数学（理）WORD 版含答案（已校对）） 设ABC ?的内角 ,,A B C 的对边分别为,,a b c ,()()a b c a b c ac ++-+=. (I)求B (II)若31 sin sin 4 A C = ,求C . 【答案】 ③三角不等式

Lesson10 Bunkering

English Listening and Speaking for (Senior) Duty Motormen （高级）值班机工英语听力与会话 姓名：________________班级：________________ 成绩：__________________ Lesson10 Bunkering Task 1 Picture Listening Look at the pictures,listen carefully and choose what you hear. 1. 2. A. Oil separator. B. Oily water separator. B.C. Fresh water generator. D. Incinerator. 3. 4. 3. A.Sea water system. B.Lube oil system. C.Jacket water system. D.Fuel oil system. 5. 6. A.Intermediate shaft . B.Crankshaft. C.Tailshaft. D.Camshaft. 7.8. A.Fuel oil system. B.Sea water system. C.Lube oil system. D.Cylinder oil system. 4. A.Fix pitch propeller. B.Controllable propeller. C.Bow thruster. D.Vane. 6. A.Propeller B.Bow thruster. C.Vane. D.Pitch

哈密市高三实验班培优教案设计设计：“影响农业发展的条件”分析及考查

“影响农业发展的条件”分析及考查设问归类 影响农业发展的条件可分为自然条件和社会经济条件(如图），自然条件有气候、地形、土壤、水源等，可以概括为“光、热、水、土、地形”，社会经济条件有市场、政策、劳动力和政策等，自然因素主要决定农作物的分布、熟制等，社会经济因素主要决定农业生产的发展和布局。 一、影响农业发展的条件分析 1.自然条件 气候：太阳辐射能、适当的温度和水分是自然界生物生长的三大要素。光热、降水等气候条件，特别是光热条件与农作物种类的分布、复种制度和产量关系最密切。因为太阳光热是植物物质形成的最基本因素。所以，农业生产的各种措施都在于因地制宜，充分合理地利用光热条件。世界农业发达的地区主要分布在热量条件和降水条件配合较好的热带和温带地区。 水源：水源因素是对天然降水的补充，对一般地区而言，它仅是作物稳产、高产的重要条件。但对干旱地区的绿洲农业、灌溉农业来说，却是作物生长和分布的决定性因素。在年降水量少于250mm的干旱地区，除有灌溉水源外，一般不能发展种植业。 地形：地形的坡度、平坦程度、地块大小等直接影响农业生产的操作和技术改造，影响农业机械化、水利化的实现。地势高低、山脉走向及坡向的差异，也直接或间接影响农业生产。 土壤：是作物生长的物质基础，直接供给作物养分。不同的土壤条件，决定了农作物的种类及其产量。世界各大洲的温带草原和肥沃的冲积平原，多半是农业发达的地区。 2.社会经济条件 国家的政策和措施：国家的政策和措施是人为的、可变的，政策和措施符合客观规律，就能促进农业生产的发展；反之，则会使农业生产遭到损失和破坏。从这个意义来说，它对农业生产的发展和布局起着决定作用。

圆培优题

六年级上册圆培优题 圆 ?易错题 1、两个圆的半径比是2:3，他们的直径比是（ ），周长比是（ ）。 2、一个圆的直径扩大到原来的2倍，它的半径就扩大到原来（ ）倍，它的周长扩大到原来的（ ）倍。 3、一座石英钟的时针长6cm ，经过6小时，这时针的尖端所走的路程是（ ）cm ，经过12小时，这时针的尖端所走的路程是（ ）cm 4、周长相等的正方形，长方形和圆，面积最大的是（ ），最小的是（ ）。 5、将一个圆，沿半径剪开，得到若干个小扇形，然后拼成一个近似的长方形。这个长方形的长是圆的（ ），宽是圆的（ ）。如果这个长方形的宽是3cm ，那么这个长方形的长是（ ）cm,周长是（ ）cm ，面积是（ ）平方厘米。如果拼成的长方形的长为12.56dm ，那么原来圆的面积是（ ）cm 2 6、小圆的半径是大圆半径的3 1，小圆的面积是大圆面积的（ ）。 7、一张正方形的周长是16分米，把它剪成一个最大的圆，剪去部分的面积是（ ）平方分米。 8、有一半圆的周长是25.7cm ，它的面积是（ ）平方厘米。 9、在一块直径是1.2米的圆形桌布周围缝在一条花边，接头处长6厘米，这条花边长（ ）米。 10、用一根12.56dm 长的铁丝弯成一个圆形铁环，这个铁环的直径是（ ）dm ，面积是（ ）dm 2 求阴影部分的面积与周长

例1、求下面图形中阴影部分的面积与周长。 练2、.如图，四个扇形的半径相等， 3、如图所示，正方形的面积是18dm2，求阴影部分的面积。(单位:厘米) 求圆的面积。

4、.如图，大正方形的边长为6厘米，小正方形的边长为4厘米求阴影部分的面积。 5、求阴影部分的面积。(单位:厘米) 半圆的周长 例1、有一个半圆形的零件如图所示，周长是25.7厘米，求这个半圆形零件的面积。 练1、如图所示，这个四分之一园的周长是17.85厘米，求它的面积。

高考数学导数与三角函数压轴题综合归纳总结教师版

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它与原点的距离是0r =>，那么sin ,cos y x r r αα==， ()tan ,0y x x α= ≠，cot x y α=(0)y ≠，sec r x α=()0x ≠，()csc 0r y y α=≠。 三角函数值只与角的大小有关，而与终边上点P 的位置无关。 三角函数线的特征：正弦线MP“站在x 轴上(起点在x 轴上)”、余弦线OM“躺在x 轴上(起点是原点)”、正切线AT“站在点(1,0)A 处(起点是A )” 同角三角函数的基本关系式： 1. 平方关系：222222sin cos 1,1tan sec ,1cot csc αααααα+=+=+= 2. 倒数关系：sin αcsc α=1,cos αsec α=1,tan αcot α=1, 3. 商数关系：sin cos tan ,cot cos sin αα αααα = = 注意：1.角α的任意性。 2.同角才可使用。 3.熟悉公式的变 形形式。 三角函数诱导公式：“ （2 k πα+）”记忆口诀: “奇变偶不变，符号看象限” 典型例题 例1．求下列三角函数值： （1）cos210o； (2)sin 4 5π 例2．求下列各式的值： （1）sin(－3 4π )； (2)cos(－60o)－sin(－210o) 例3．化简 ) 180sin()180cos() 1080cos()1440sin(?--?-?-?-?+?αααα

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高中部实验班实施方案 -CAL-FENGHAI-(2020YEAR-YICAI)_JINGBIAN

潮阳新世界中英文学校高中部 实验班实施方案 一、指导思想： 为进一步推进教学改革，培养拔尖创新型人才，打造高端质量，形成品牌效应，学校在高中各年级成立拔尖创新型人才培养实验班，探索高中阶段进行拔尖创新型人才培养的有效途径，实现学校内涵发展。 二、办学目标： 1、打造高端质量：实验班一批升学率达85%，本科率100%，五大名校升学率达10%，1人以上进入全市高考前30名，力争1人以上考上清华北大。重点班一批升学率55%，本科率100%，1人以上考上五大名校。 2、形成品牌效应：以优秀的学生团队、一流的班风学风、先进的教学理念、高效的管理模式，打造高端质量，形成品牌效应，吸引优质生源。 3、促进教学改革：大力推进教学改革创新，促进教师观念转变，在优生培养上努力学习先进的教学理念，大胆探索高效的培养方法，形成校本特色的教学管理模式。 三、班级组建： 1、根据生源素质确定每届文理实验班数量，实施小班化教学，学校坚持公平公正的原则，严格按成绩选拔，确保最优秀的生源质量。 2、实验班实行动态管理，引入竞争机制：在高一开学前根据中考成绩择优录取组建班级；高一上学期末文理分科后，根据学生成绩及综合表现，择优选拔重新分班，保持相对稳定；在高三开学前根据学生成绩及综合表现，按10%比例实行进出机制，即实验班排名在后10%的同学退到平行班，平行班排名在前10%的同学进入实验班。 四、师资配备： 择优配备实验班班主任和教师，实施竞争上岗。遴选有高尚人格魅力、强烈事业进取心和突出班级管理能力的优秀老师担任实验班班主任；竞选师德高尚、理念先进、业务精湛、能吃苦耐劳、执行力强的优秀教师组建实验班教师团队。 五、教学策略： 1、调整时间安排：实验班从高一开始，每天上8节正课，每晚上4节自习课。增加 高考科目课时、学生自主学习时间及训练课时比重，适当缩减学业水平考试科目课时，减少教师课堂讲授时间比重，充分占有时间先机。 2、优化课程设置：实验班的课程设置要在国标课程基础上进一步优化，各学科的教 师均依据课标要求，按照学科主干知识与能力要点制定具体的学科教与学计划。适当引入新概念英语及数理化竞赛辅导等课程，在夯实基础的同时，增加知识输入和储备量，强化学生思维能力和实战能力培养。 3、创新教学方式：大力推进课堂教学改革，努力实践新课改要求，利用最先进的教 学手段，善于开展启发式、探究式、讨论式、读研式、自学式、活动式教学，激发学生的好奇心和求知欲望，培养学生浓厚的学习兴趣和问题意识，引导学生主动参与、积极思考、大胆质疑，着力提高独立思考和自主学习的能力和品质。充分调动学生积极性，注重师生互动、生生互动，鼓励学生相互质疑解惑，构建更加开放生动、充满活力的课堂。 教师要采用符合实验班学生特点的导学案制，切实做到分层教学，分层练习，注重知识的拓宽加深，使优秀学生吃饱喝足。 4、强化能力训练：实行“日练周测月考”制。对实验班单独命题，单独布置作业， 单独制卷考查。坚决落实精讲多练精炼原则，大力强化学生实战能力。 （1）日练：教师在充分钻研课标、教材、学情的基础上备课。讲授上对原理的剖析，范例的讲解，每节课不超过25分钟，学生练习巩固，学情反馈，纠错，每节课不少于15分钟。 2

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一、圆的综合真题与模拟题分类汇编（难题易错题） 1．如图1，将长为10的线段OA绕点O旋转90°得到OB，点A的运动轨迹为AB，P是半径OB上一动点，Q是AB上的一动点，连接PQ. 发现：∠POQ＝________时，PQ有最大值，最大值为________； 思考：（1）如图2，若P是OB中点，且QP⊥OB于点P，求BQ的长； （2）如图3，将扇形AOB沿折痕AP折叠，使点B的对应点B′恰好落在OA的延长线上，求阴影部分面积； 探究：如图4，将扇形OAB沿PQ折叠，使折叠后的弧QB′恰好与半径OA相切，切点为C，若OP＝6，求点O到折痕PQ的距离． 【答案】发现： 90°，102；思考：（1） 10 3 π =；（2）25π?1002+100；（3）点O 到折痕PQ的距离为30. 【解析】 分析：发现：先判断出当PQ取最大时，点Q与点A重合，点P与点B重合，即可得出结论； 思考：（1）先判断出∠POQ=60°，最后用弧长用弧长公式即可得出结论； （2）先在Rt△B'OP中，OP2+(102?10)2=（10-OP）2，解得OP=102?10，最后用面积的和差即可得出结论． 探究：先找点O关于PQ的对称点O′，连接OO′、O′B、O′C、O′P，证明四边形OCO′B是矩 形，由勾股定理求O′B，从而求出OO′的长，则OM=1 2 OO′=30． 详解：发现：∵P是半径OB上一动点，Q是AB上的一动点，∴当PQ取最大时，点Q与点A重合，点P与点B重合， 此时，∠POQ=90°，PQ=22 OA OB +=102； 思考：（1）如图，连接OQ， ∵点P是OB的中点，

∴OP= 12OB=1 2OQ ． ∵QP ⊥OB ， ∴∠OPQ=90° 在Rt △OPQ 中，cos ∠QOP=1 2 OP OQ =， ∴∠QOP=60°， ∴l BQ = 601010 1803 ππ?=； （2）由折叠的性质可得，BP ＝B ′P ，AB ′＝AB ＝102， 在Rt △B'OP 中，OP 2+(102?10)2=（10-OP ）2 解得OP=102?10， S 阴影=S 扇形AOB -2S △AOP =290101 210(10210)3602 π?-???- ＝25π?1002+100； 探究：如图2，找点O 关于PQ 的对称点O′，连接OO′、O′B 、O′C 、O′P ， 则OM=O′M ，OO′⊥PQ ，O′P=OP=3，点O′是B Q '所在圆的圆心， ∴O′C=OB=10， ∵折叠后的弧QB′恰好与半径OA 相切于C 点， ∴O′C ⊥AO ， ∴O′C ∥OB ， ∴四边形OCO′B 是矩形， 在Rt △O′BP 中，226425-= 在Rt △OBO′K ，2210(25)=230-， ∴OM= 12OO′=1 2 ×23030 即O 到折痕PQ 30 点睛：本题考查了折叠问题和圆的切线的性质、矩形的性质和判定，熟练掌握弧长公式l= 180 n R π（n 为圆心角度数，R 为圆半径），明确过圆的切线垂直于过切点的半径，这是常考的性质；对称点的连线被对称轴垂直平分．