题干

如图,在⊙O中,AD是直径,弧AB=弧AC,求证:AO平分∠BAC.

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答案(点此获取答案解析)

解:∵弧AB=弧AC,

∴∠AOB=∠AOC,

在△AOB与△AOC中,

OA=OA,∠AOB=∠AOC,OB=OC,

∴△AOB≌△AOC(SAS).

∴∠OAB=∠OAC.

∴AO平分∠BAC.

同类题4

阅读理解

    An "apple polisher" is one who gives gifts to win friendship or special treatment.It is not exactly a bribe(贿赂), but is close to it.

    All sorts of people are apple polishers,including politicians and people in high offices—just about everybody. Oliver Cromwell,the great English leader,offered many gifts to win the support of George Fox and his party,but failed.

    There are other phrases meaning the same thing as "apple-polishing"—"soft-soaping" or "butter-up".A gift is just one way to "soft-soap" somebody,or to "butter him up".Another that is just as effective is flattery,giving someone high praise—telling him how good he looks,or how well he speaks,or how talented and wise he is.

    Endless are the ways of flattery.Who does not love or hear it?Only an unusual man can resist the thrill of being told how wonderful he is.In truth,flattery is good medicine for most of us,who gets so little of it.

    We need it to be more sure of ourselves.It cannot hurt unless we get carried away by it.But we just lap it up for its food value and nourishment,as a cat laps up milk,then we can still remain true to ourselves.

    Sometimes,however,flattery will get you nothing from one who has had too much of it.A good example is the famous 12th century legend of King Canute of Denmark and England.The king got tired of listening to the endless sickening flattery of his courtiers(朝臣).They over-praised him to the skies,as a man of limitless power.

    He decided to teach them a lesson.He took them to the seashore and sat down.Then he ordered the waves to stop coming in.The tide was too busy to listen to him.The king was satisfied.This might show his followers how weak his power was and how empty their flattery.

同类题5

阅读下面的文字,完成下面小题.

百年震柳

梁衡

    ①1920年12月16日,在宁夏海原县发生了一场全球最大的地震。是晚8时,风暴大起,四野尘霾,大地颤动,山移、地裂、河断、城陷。黄土高原经这一抖,如骨牌倒地,土块横飞。老百姓惊呼:“山走了!”有整座山滑行三四公里者,最大滑坡面积竟毗连三县,达两千平方公里。山一倒就瞬间塞河成湖,形成无数的大小“海子”。地震中心原有一大盐湖,为西北重要的产盐之地。湖底突然鼓起一道滚动的陡坎,如有人在湖下推行,竟滴水不漏地将整个湖面向北移了一公里,称之为“滚湖”。所有的地标都被扭曲、翻腾得面目全非。大地瞬间裂开一条237公里长的大缝,横贯甘肃、陕西、宁夏。裂缝如闪电过野,利刃破竹,见山裂山,见水断水,将城池村庄一劈两半,庄禾田畴被撕为碎片。当这条闪电穿过海原县的一条山谷时,谷中正有一片旺盛的柳树,它照样噼噼啪啪,一路撕了下去。但是没有想到,这些柔枝弱柳,虽被摇得东倒西歪,断枝拔根,却没有气绝身死。狂震之后,有一棵虽被撕为两半,但又挺起身子,顽强地活了下来,至今仍屹立在空谷之中,这就是那棵有名的震柳。

    ②我不知道这株柳,该称它是一棵还是两棵。它同根,同干,同样的树纹,头上还枝叶连理。但地震已经将它从下一撕为二,现在两个半边树中间可穿行一人,而每一半也都有合抱之粗了。人老看脸,树老看皮。经过百年岁月的煎熬,这树皮已如老人的皮肤,粗糙,多皱,青筋暴突。纹路之宽可容进一指,东奔西突,似去又回,一如黄土高原上的千沟万壑。这棵树已经有500年,就是说地震之时它已是400岁的高龄,而大难后至今又过了100岁。

    ③看过树皮,再看树干的开裂部分,真让你心惊肉跳。平常,锯开一根木头,无论从哪个方向切入,那剖面上的年轮图案都幻化无穷,美不胜收,以至于木纹装饰成了我们生活中不可或缺的风景,木纹之美也成了生命之美的象征。但是现在,面对树心我找不到一丝的年轮。如同五马分尸,地裂闪过,先是将树的老根嘎嘎嘣嘣地扯断,又从下往上扭裂、撕剥树皮,然后再将树心的木质部分撕肝裂肺,横扯竖揪,惨不忍睹。但是这棵树并没有死。地震揪断了它的根,却拔不尽它的须;撕裂了它的躯干,却扯不断它的连理枝。灾难过后,它又慢慢地挺了过来。百年来,在这人迹罕至的桃源深处,阳光暖暖地抚慰着它的身子,细雨轻轻地冲洗着它的伤口,它自身分泌着汁液,小心地自疗自养,生骨长肉。百年的疤痕,早已演化成许多起伏不平的条、块、洞、沟、瘤,像一块凝固的岩石,为我们定格了一段难忘的岁月。

    ④柳树这个树种很怪。论性格,它是偏于柔弱一面的,枝条柔韧,婀娜多姿,多生水边。所以柳树常被人作了多情的象征。唐人有折柳相送的习俗,取其情如柳丝,依依不舍。贺知章把柳比作窈窕的美人:“碧玉妆成一树高,万条垂下绿丝绦。不知细叶谁裁出,二月春风似剪刀。”但在关键时刻,这个弱女子却能以柔克刚,表现出特别的顽强。西北的气候寒冷干旱,是足够恶劣的了,它却能常年扎根于此o在北国的黄土地上,柳树是春天发芽最早、秋天落叶最迟的树,它尽力给大地最多的绿色。当年左宗棠进军西北,别的树不要,却单选中这弱柳与大军同行。“新栽杨柳三千里,引得春风度玉关。”柳树有一种特殊的本领,遇土即根,有水就长,干旱时就休息,苦熬着等待天雨,但绝不会轻生去死。它的根系特别发达,能在地下给自己铺造一个庞大的供水系统,远远地延伸开去,捕捉哪怕一丝丝的水汽。它木性软,常用来做案板,刀剁而不裂;枝性柔,立于行道旁,风吹而不折。

    ⑤我想,海原大地震的震波绕地球三圈,移山填河,夺去了28万人的生命,而这一株裂而不死的古柳却能够存活下来,它肯定是要对后人说点什么。

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