题干

已知:如图,MN、PQ是⊙O的两条弦,且QN=MP, 求证:MN= PQ.


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答案(点此获取答案解析)

证明:∵QN=MP,∴ 弧QN=弧MP,∴弧MN=弧PQ,∴MN=PQ

同类题2

阅读下面的文字,完成文后各题。

放鸭

莫言

    青草湖里鱼虾很多,水草繁茂。青草湖边人家古来就有养鸭的习惯。这里出产的鸭蛋个大双黄多,半个省都有名。有些年,因为“割资本主义尾巴”,湖上鸭子绝了迹。这几年政策好了,湖上的鸭群像一簇簇白云。

    李老壮是养鸭专业户,天天撑着小船赶着鸭群在湖上漂荡。

    这天,对面来了个赶着鸭群的姑娘。姑娘鸭蛋脸儿,黑葡萄眼儿,渔歌儿唱得脆响,像在满湖里撒珍珠。

    两群鸭子齐头并进,姑娘在船上递话过来:

    “大伯,您是哪个村的——”

    “湖东李村,”老壮瓮声瓮气地回答,“你呐,姑娘?”

    “湖西王庄。”

    “大伯,你们村有个李老壮吗?”

    “有这么个人,你问他干什么?”

    姑娘的脸红了红,上嘴唇咬咬下嘴唇,说:“没事,随便问问。”

    “听说李老壮手脚不太干净,前几年偷队里的鸭子被抓住,在湖东八个村里游过乡?”

    “游过。”老壮掉过船头,把鸭子撵得惊飞起来。

    姑娘提起的这件事戳到了李老壮的伤疤上。“四人帮”横行那些年,上头下令,不准个人养鸭,李老壮家那十几只鸭子被生产队里“共了产”,家里的油盐钱全靠抠这几只鸭屁股啊!他深更半夜摸到鸭棚里提了两只鸭子——运气不济——当场被巡夜的民兵抓住了。为这事老壮差点上了吊。

    姑娘提起这事,不由老壮不窝火。从此,他对她起了反感。他尽量避免和她碰面,实在躲不过了,也爱理不理地冷落人家。姑娘还是那么热情,那么开朗。一见面,先送他一串银铃样的笑声,再送他一堆蜜甜的大伯。老壮面子上应付着,心里却在暗暗地骂:瞧你那个鲤鱼精样子,浪说浪笑,不是好货!

    有一天,晴朗的天空突然布满了乌云,雷鸣电闪地下了一场暴雨。李老壮好不容易才拢住鸭群。暴雨过后,在一片芦苇边上,老壮碰到了十几只鸭子。他知道这一定是刚才的暴风雨把哪个放鸭人的鸭群冲散了。“好鸭!”老壮不由地赞了一声。只见这十几只鸭子浑身雪白,身体肥硕,像一只只小船儿在水面上漂荡,十分招人喜爱。老壮突然想起在湖西王庄公社农技站工作的儿子说过,他们刚从京郊引进了一批良种鸭,大概就是这些吧?老壮一边想着,一边把这十几只肥鸭赶进自己的鸭群。

    第二天,老壮一进湖就碰上了王庄的放鸭姑娘。

    “大伯,你看没看到十几只鸭子?昨儿个的暴风雨把我的鸭群冲散了,回家一点数,少了十四只。是刚从农技站买的良种鸭,把我急得一夜没睡好觉呢!”

    老壮看到姑娘那着急的样子,早已忘记了前些日子的不快,用手一指鸭群,说:”那不是,一只也不少,都在我这儿呢。

    “太谢谢您啦,大伯。我把鸭赶过来吧?”

    “我来。”李老壮挥动竹篙,把那十四只白鸭从自家鸭群里轰出来。放鸭姑娘“呷呷”的唤着,白鸭归了群。

    “大伯,咱们在一个湖里放了大半年鸭子,俺还不知道您姓甚名谁呢!”姑娘把小船撑到老壮的小船边,用唱歌般的发音发问。

    “姓李,名老壮!”

    “呀!您就是苇林、李苇林,不,李技术员的……”

    “不差,我就是李苇林他爹,”李老壮胡子翘起来,“我就是那个因为偷鸭子游过乡的李老壮!”

    姑娘又一次惊叫起来。她双眼瞪得杏子圆,脸红成了一朵粉荷花。

    “大伯,谢谢您……”她匆匆忙忙地对着老壮鞠了一躬,撑着船,赶着鸭,没命地逃了。

    “姑娘,你认识我家苇林?见到他捎个话儿,让他带几只良种鸭回来!”李老壮高声喊着。

    李老壮长舒了一口气,感到十分轻松愉快。他自言自语地说:“这姑娘,真好相貌,人品也好,怪不得人说青草湖边出美人呢!”

同类题4

根据短文理解,选择正确答案。

    A student was one day taking a walk with his teacher. As they went along, they saw a pair of old shoes lying in the path. They were a poor farmer's, who was working in the nearby field.

    The student turned to the teacher, saying: “we will hide his shoes, and hide ourselves behind those trees, and wait to see what he will do.”

    “My young friend,” answered the teacher, “we should never make fun of the poor. Why not put a coin in each shoe, and then we will hide ourselves and watch?” The student did so and they both hid themselves behind the trees. The poor man soon finished his work, and came across the field to the path where he had left his coat and shoes.

    After putting on his coat, he put his foot into one of his shoes, and felt something hard. Then he bent (弯腰) down to feel what it was, and found the coin. Surprised, he looked at the coin, turned it around and looked at it again. He then looked around, but no person was seen. He put the money into his pocket, and continued to put on the other shoe. His surprise was doubled on finding the other coin.

    He couldn't control his feelings and fell to his knees, looked up to the sky and expressed his thanks. Then he spoke of his wife, sick and helpless, and his children without bread. He said the help would save them from dying.

    The student stood there deeply moved, and his eyes filled with tears. “Now,” said the teacher, “are you not much happier than if you had hidden the shoes?”