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九年级数学圆复习教学案(吐血制作)

发布时间:2013-12-28 10:39:31  

成都起航教育个性化教育教案

教师: 宋涛 学生: 康雪怡 年级: 九年级 科目: 数学

时间: 20 13 年 11 月 24 日 圆 课次: 10

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成都起航教育个性化教育教案

质量至上 精益求精

成都起航教育个性化教育教案

质量至上 精益求精

成都起航教育个性化教育教案

质量至上 精益求精

成都起航教育个性化教育教案

质量至上 精益求精

成都起航教育个性化教育教案

质量至上 精益求精

成都起航教育个性化教育教案

质量至上 精益求精

?? 成都起航教育个性化教育教案 一、教学目的与考点分析

经典例题透析

1.垂径定理及其应用

在圆这一章中,涉及垂径定理的有关知识点很多,如弓形中的有关计算、切线的性质、判定定理等,也是在各地中考中经常出现的一个考点.应用垂径定理可以进行线段的垂直、平分以及弓形面积的计算等.

1.某居民小区的一处圆柱形的输水管道破裂,维修人员为更换管道,需要确定管道圆形截面的半径,如图所示是水平放置的破裂管道有水部分的截面.

?? INCLUDEPICTURE "http://video.etiantian.com/security/9d6bb1eee1894ab4e402b4d8c40cdcbe/4cda95c7/ett20/resource/d4ebace7491106c9a0b23a76722235a5/jdlt.files/image001.jpg" \* MERGEFORMATINET ??????

(1)请你补全这个输水管道的圆形截面图;

(2)若这个输水管道有水部分的水面宽AB=16cm,水最深的地方的高度为4cm,求这个圆形截面的半径.

总结升华:在解答有关圆的问题时,常需要运用图中已知条件寻找线段之间、角之间、弧之间的关系,从中探索出如等腰三角形、直角三角形等信息,从而达到解决问题的目的,此题还可以进一步求出阴影部分的周长或面积等.

举一反三:

【变式1】“圆材埋壁”是我国古代著名的数学著作《九章算术》中的问题:“今有圆材,埋在壁中,不知大小,以锯锯之,深一寸,锯道长一尺,问径几何?”用数学语言可表示为:如图所示,CD为⊙O的直径,弦AB⊥CD于E,CE=1寸,AB=10寸,则直径CD的长为( )

?? INCLUDEPICTURE "http://video.etiantian.com/security/9d6bb1eee1894ab4e402b4d8c40cdcbe/4cda95c7/ett20/resource/d4ebace7491106c9a0b23a76722235a5/jdlt.files/image009.jpg" \* MERGEFORMATINET ??????

A.12.5寸 B.13寸 C.25寸 D.26寸

2.圆周角及其应用

MERGEFORMATINET INCLUDEPICTURE "http://video.etiantian.com/fav.gif" \*

圆周角与圆心角是本章中最常用的角,在中考中经常出现,一般单独考查它的题目不多,都是隐含在其他题目中.

?? INCLUDEPICTURE "http://video.etiantian.com/security/9d6bb1eee1894ab4e402b4d8c40cdcbe/4cda95c7/ett20/resource/d4ebace7491106c9a0b23a76722235a5/images/mb04_080317.gif" \* MERGEFORMATINET ??????2.如图所示,△ABC内接于⊙O,点D是CA延长线上一点,若∠BOC=120°,∠BAD等于( )?? INCLUDEPICTURE "http://video.etiantian.com/fav.gif" \* MERGEFORMATINET ?????? ?? INCLUDEPICTURE "http://video.etiantian.com/security/9d6bb1eee1894ab4e402b4d8c40cdcbe/4cda95c7/ett20/resource/d4ebace7491106c9a0b23a76722235a5/jdlt.files/image013.jpg" \* MERGEFORMATINET ??????

A.30° B.60° C.75° D.90°

举一反三:

【变式1】如图所示,⊙O的内接四边形ABCD中,AB=CD,则图中与∠1相等的角有________________.

?? INCLUDEPICTURE "http://video.etiantian.com/security/9d6bb1eee1894ab4e402b4d8c40cdcbe/4cda95c7/ett20/resource/d4ebace7491106c9a0b23a76722235a5/jdlt.files/image017.jpg" \* MERGEFORMATINET ??????

【变式2】如图所示,已知AB为⊙O的直径,AC为弦,OD∥BC,BC=4cm. ?? (1)说明AC⊥OD;

(2)求OD的长.

?? 成都起航教育个性化教育教案

INCLUDEPICTURE 3.切线的性质及判定

"http://video.etiantian.com/fav.gif" \* MERGEFORMATINET

涉及圆的切线的问题在各地中考中以各种题型出现,主要考查切线的识别方法、切线的特征以及对切线的应用能力,所以应认真理解有关切线的内容,并能用来解答实际问题.

?? INCLUDEPICTURE "http://video.etiantian.com/security/9d6bb1eee1894ab4e402b4d8c40cdcbe/4cda95c7/ett20/resource/d4ebace7491106c9a0b23a76722235a5/images/mb04_080317.gif" \* MERGEFORMATINET ??????3.如图所示,直线MN是⊙O的切线,A为切点,过A的作弦交⊙O于B、C,连接BC,证明∠NAC=∠B.?? INCLUDEPICTURE "http://video.etiantian.com/fav.gif" \* MERGEFORMATINET ??????

?? INCLUDEPICTURE "http://video.etiantian.com/security/9d6bb1eee1894ab4e402b4d8c40cdcbe/4cda95c7/ett20/resource/d4ebace7491106c9a0b23a76722235a5/jdlt.files/image021.jpg" \* MERGEFORMATINET ??????

举一反三:

【变式1】如图所示,DB切⊙O于点A,∠AOM=66°,则∠DAM=________________. ?? INCLUDEPICTURE "http://video.etiantian.com/security/9d6bb1eee1894ab4e402b4d8c40cdcbe/4cda95c7/ett20/resource/d4ebace7491106c9a0b23a76722235a5/jdlt.files/image023.jpg" \* MERGEFORMATINET ??????

【变式2】如图所示,AB是⊙O的直径,?? INCLUDEPICTURE "http://video.etiantian.com/security/9d6bb1eee1894ab4e402b4d8c40cdcbe/4cda95c7/ett20/resource/d4ebace7491106c9a0b23a76722235a5/jdlt.files/image025.gif" \* MERGEFORMATINET ??????是⊙??O的切线,C是切点,过A、B分别作?? INCLUDEPICTURE "http://video.etiantian.com/security/9d6bb1eee1894ab4e402b4d8c40cdcbe/4cda95c7/ett20/resource/d4ebace7491106c9a0b23a76722235a5/jdlt.files/image025.gif" \* MERGEFORMATINET ??????的垂线,垂足分别为E、F,证明EC=CF.

?? INCLUDEPICTURE "http://video.etiantian.com/security/9d6bb1eee1894ab4e402b4d8c40cdcbe/4cda95c7/ett20/resource/d4ebace7491106c9a0b23a76722235a5/images/mb04_080317.gif" \* MERGEFORMATINET ??????4.如图所示,EB、BC是⊙O是两条切线,B、C是切点,A、D是⊙O上两点,如果∠E=46°,∠DCF=32°,那么∠A的度数是________________.?? INCLUDEPICTURE "http://video.etiantian.com/fav.gif" \* MERGEFORMATINET ??????

?? INCLUDEPICTURE "http://video.etiantian.com/security/9d6bb1eee1894ab4e402b4d8c40cdcbe/4cda95c7/ett20/resource/d4ebace7491106c9a0b23a76722235a5/jdlt.files/image028.jpg" \* MERGEFORMATINET ?????? 答案:99°.

解析:由EB=EC,∠E=46°知,∠ECB= 67°,从而∠BCD=180°-67°-32°=81°, 在⊙O中,∠BCD与∠A互补,所以∠A=180°-81°=99°.

举一反三:

【变式1】如图所示,已知在△ABC中,∠B=90°,O是AB上一点,以O为圆心、OB为半径的圆与AB交于点E,与AC切于点D.求证:DE∥OC;

??

质量至上 精益求精

?? 成都起航教育个性化教育教案

INCLUDEPICTURE "http://video.etiantian.com/fav.gif" 4.两圆位置的判定

\* MERGEFORMATINET

在各地中考试题中,单独考查点与圆、直线与圆、圆与圆的位置关系的题目一般多以选择题、填空题为主,在解答题、探究题中也经常作为主要考查目标,这部分内容不仅考查基础知识,而且考查综合运用能力.

?? INCLUDEPICTURE "http://video.etiantian.com/security/9d6bb1eee1894ab4e402b4d8c40cdcbe/4cda95c7/ett20/resource/d4ebace7491106c9a0b23a76722235a5/images/mb04_080317.gif" \* MERGEFORMATINET ??????5.填空题?? INCLUDEPICTURE "http://video.etiantian.com/fav.gif" \* MERGEFORMATINET ??????

(1)已知圆的直径为13 cm,圆心到直线?? INCLUDEPICTURE "http://video.etiantian.com/security/9d6bb1eee1894ab4e402b4d8c40cdcbe/4cda95c7/ett20/resource/d4ebace7491106c9a0b23a76722235a5/jdlt.files/image025.gif" \* MERGEFORMATINET ??????的距离为6cm,那么直线?? INCLUDEPICTURE "http://video.etiantian.com/security/9d6bb1eee1894ab4e402b4d8c40cdcbe/4cda95c7/ett20/resource/d4ebace7491106c9a0b23a76722235a5/jdlt.files/image025.gif" \* MERGEFORMATINET ??????和这个圆的公共点的个数是______.

(2)两个圆内切,其中一个圆的半径为5,两圆的圆心距为2,则另一个圆的半径是_______________.

【变式2】已知两圆的圆心距?? INCLUDEPICTURE "http://video.etiantian.com/security/9d6bb1eee1894ab4e402b4d8c40cdcbe/4cda95c7/ett20/resource/d4ebace7491106c9a0b23a76722235a5/jdlt.files/image035.gif" \* MERGEFORMATINET ??????为3,?? INCLUDEPICTURE "http://video.etiantian.com/security/9d6bb1eee1894ab4e402b4d8c40cdcbe/4cda95c7/ett20/resource/d4ebace7491106c9a0b23a76722235a5/jdlt.files/image036.gif" \* MERGEFORMATINET ??????的半径为1.?? INCLUDEPICTURE "http://video.etiantian.com/security/9d6bb1eee1894ab4e402b4d8c40cdcbe/4cda95c7/ett20/resource/d4ebace7491106c9a0b23a76722235a5/jdlt.files/image037.gif" \* MERGEFORMATINET ??????的半径为2,则?? INCLUDEPICTURE "http://video.etiantian.com/security/9d6bb1eee1894ab4e402b4d8c40cdcbe/4cda95c7/ett20/resource/d4ebace7491106c9a0b23a76722235a5/jdlt.files/image036.gif" \* MERGEFORMATINET ??????与?? INCLUDEPICTURE

"http://video.etiantian.com/security/9d6bb1eee1894ab4e402b4d8c40cdcbe/4cda95c7/ett20/resource/d4ebace7491106c9a0b23a76722235a5/jdlt.files/image037.gif" \* MERGEFORMATINET ??????的位置关系为________.

【变式3】在平面直角坐标系中如图所示,两个圆的圆心坐标分别是(3,0)和(0,-4),半径分别是?? INCLUDEPICTURE "http://video.etiantian.com/security/9d6bb1eee1894ab4e402b4d8c40cdcbe/4cda95c7/ett20/resource/d4ebace7491106c9a0b23a76722235a5/jdlt.files/image038.gif" \* MERGEFORMATINET ??????和?? INCLUDEPICTURE

"http://video.etiantian.com/security/9d6bb1eee1894ab4e402b4d8c40cdcbe/4cda95c7/ett20/resource/d4ebace7491106c9a0b23a76722235a5/jdlt.files/image039.gif" \* MERGEFORMATINET ??????,则这质量至上 精益求精

?? 成都起航教育个性化教育教案

两个圆的公切线有( )

A.1条 B.2条 C.3条 D.4条

5.弧长的计算及其应用

"http://video.etiantian.com/fav.gif" \* MERGEFORMATINET INCLUDEPICTURE

?? INCLUDEPICTURE "http://video.etiantian.com/security/9d6bb1eee1894ab4e402b4d8c40cdcbe/4cda95c7/ett20/resource/d4ebace7491106c9a0b23a76722235a5/images/mb04_080317.gif" \* MERGEFORMATINET ??????6.如图所示,在正方形铁皮下剪下一个圆形和扇形,使之恰好围成图中所示的一个圆锥模型,设圆的半径为r,扇形半径为R,则圆的半径与扇形半径之问的关系为( )?? INCLUDEPICTURE "http://video.etiantian.com/fav.gif" \* MERGEFORMATINET ??????

?? INCLUDEPICTURE "http://video.etiantian.com/security/9d6bb1eee1894ab4e402b4d8c40cdcbe/4cda95c7/ett20/resource/d4ebace7491106c9a0b23a76722235a5/jdlt.files/image042.jpg" \* MERGEFORMATINET ??????

A.?? INCLUDEPICTURE "http://video.etiantian.com/security/9d6bb1eee1894ab4e402b4d8c40cdcbe/4cda95c7/ett20/resource/d

4ebace7491106c9a0b23a76722235a5/jdlt.files/image043.gif" \* MERGEFORMATINET ??????

B.?? INCLUDEPICTURE "http://video.etiantian.com/security/9d6bb1eee1894ab4e402b4d8c40cdcbe/4cda95c7/ett20/resource/d

4ebace7491106c9a0b23a76722235a5/jdlt.files/image044.gif" \* MERGEFORMATINET ??????

C.?? INCLUDEPICTURE "http://video.etiantian.com/security/9d6bb1eee1894ab4e402b4d8c40cdcbe/4cda95c7/ett20/resource/d

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D.?? INCLUDEPICTURE "http://video.etiantian.com/security/9d6bb1eee1894ab4e402b4d8c40cdcbe/4cda95c7/ett20/resource/d4ebace7491106c9a0b23a76722235a5/jdlt.files/image046.gif" \* MERGEFORMATINET ??????

6.图形面积的计算及其应用

"http://video.etiantian.com/fav.gif" \* MERGEFORMATINET INCLUDEPICTURE

与圆有关的图形面积计算问题有圆的面积、扇形面积、圆柱及圆锥的侧面积与全面积.考查题型以选择题、填空题、解答题为主,考查重点是对有关公式的灵活运用.其中是不规则图形面积的计算,应首先将其转化为规则图形,然后再进行.

?? INCLUDEPICTURE "http://video.etiantian.com/security/9d6bb1eee1894ab4e402b4d8c40cdcbe/4cda95c7/ett20/resource/d4ebace7491106c9a0b23a76722235a5/images/mb04_080317.gif" \* MERGEFORMATINET ??????7.沈阳市某中学举办校园文化艺术节,小颖设计了同学们喜欢的图案“我的宝贝”,图案的一部分是以斜边长为12cm的等腰直角三角形的各边为直径作的半圆,如图所示,则图中阴影部分的面积为( )?? INCLUDEPICTURE "http://video.etiantian.com/fav.gif" \* MERGEFORMATINET ??????

?? INCLUDEPICTURE "http://video.etiantian.com/security/9d6bb1eee1894ab4e402b4d8c40cdcbe/4cda95c7/ett20/resource/d4ebace7491106c9a0b23a76722235a5/jdlt.files/image048.jpg" \* MERGEFORMATINET ??????

A.?? INCLUDEPICTURE "http://video.etiantian.com/security/9d6bb1eee1894ab4e402b4d8c40cdcbe/4cda95c7/ett20/resource/d

4ebace7491106c9a0b23a76722235a5/jdlt.files/image049.gif" \* MERGEFORMATINET ??????

B.72?? INCLUDEPICTURE "http://video.etiantian.com/security/9d6bb1eee1894ab4e402b4d8c40cdcbe/4cda95c7/ett20/resource/d

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C.36?? INCLUDEPICTURE "http://video.etiantian.com/security/9d6bb1eee1894ab4e402b4d8c40cdcbe/4cda95c7/ett20/resource/d质量至上 精益求精

?? 成都起航教育个性化教育教案

4ebace7491106c9a0b23a76722235a5/jdlt.files/image051.gif" \* MERGEFORMATINET ??????

D.72?? INCLUDEPICTURE "http://video.etiantian.com/security/9d6bb1eee1894ab4e402b4d8c40cdcbe/4cda95c7/ett20/resource/d4ebace7491106c9a0b23a76722235a5/jdlt.files/image051.gif" \* MERGEFORMATINET ??????

7.圆与其他知识的综合运用

"http://video.etiantian.com/fav.gif" \* MERGEFORMATINET INCLUDEPICTURE

?? INCLUDEPICTURE "http://video.etiantian.com/security/9d6bb1eee1894ab4e402b4d8c40cdcbe/4cda95c7/ett20/resource/d4ebace7491106c9a0b23a76722235a5/images/mb04_080317.gif" \* MERGEFORMATINET ??????8.如图所示,已知灯塔A的周围7海里的范围内有暗礁,一艘渔船在B处测得灯塔A在北偏东60°的方向,向正东航行8海里到达C处后,又测得该灯塔在北偏东30°的方向,渔船如果不改变方向,继续向东航行,有没有触的礁危险??? INCLUDEPICTURE "http://video.etiantian.com/fav.gif" \* MERGEFORMATINET ??????

?? INCLUDEPICTURE "http://video.etiantian.com/security/9d6bb1eee1894ab4e402b4d8c40cdcbe/4cda95c7/ett20/resource/d4ebace7491106c9a0b23a76722235a5/jdlt.files/image060.jpg" \* MERGEFORMATINET ??????

思路点拨:若渔船在向东航行的过程中的每一位置到A点的距离都大于7海里,则不会进入危险区域,所以只要计算航线上到A点最近的点与A点的距离.

解:过点A作AD⊥BC交直线BC于D,设AD=x海里.

∵ ∠ABD=90°-60°=30°,∠ACD=90°-30°=60°,

∴ AB=2x,AC=2CD.

∴ ?? INCLUDEPICTURE "http://video.etiantian.com/security/9d6bb1eee1894ab4e402b4d8c40cdcbe/4cda95c7/ett20/resource/d4ebace7491106c9a0b23a76722235a5/jdlt.files/image061.gif" \* MERGEFORMATINET ??????,?? INCLUDEPICTURE

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∴ ?? INCLUDEPICTURE "http://video.etiantian.com/security/9d6bb1eee1894ab4e402b4d8c40cdcbe/4cda95c7/ett20/resource/d4ebace7491106c9a0b23a76722235a5/jdlt.files/image063.gif" \* MERGEFORMATINET ??????,?? INCLUDEPICTURE

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∵ ?? INCLUDEPICTURE "http://video.etiantian.com/security/9d6bb1eee1894ab4e402b4d8c40cdcbe/4cda95c7/ett20/resource/d4ebace7491106c9a0b23a76722235a5/jdlt.files/image065.gif" \* MERGEFORMATINET ??????,∴ ?? INCLUDEPICTURE

"http://video.etiantian.com/security/9d6bb1eee1894ab4e402b4d8c40cdcbe/4cda95c7/ett20/resource/d4ebace7491106c9a0b23a76722235a5/jdlt.files/image066.gif" \* MERGEFORMATINET ??????,?? INCLUDEPICTURE

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即?? INCLUDEPICTURE "http://video.etiantian.com/security/9d6bb1eee1894ab4e402b4d8c40cdcbe/4cda95c7/ett20/resource/d4ebace7491106c9a0b23a76722235a5/jdlt.files/image068.gif" \* MERGEFORMATINET ??????.

这就是说当渔船航行到点D时,在以A为圆心、以7海里为半径的圆形暗礁内.

所以,若不改变航向继续向正东航行,有触礁的危险.

质量至上 精益求精

?? 成都起航教育个性化教育教案

总结升华:解这类实际问题,只需求其最小值或最大值,与已知数据进行比较,从而得出正确的结论.

?? INCLUDEPICTURE "http://video.etiantian.com/security/9d6bb1eee1894ab4e402b4d8c40cdcbe/4cda95c7/ett20/resource/d4ebace7491106c9a0b23a76722235a5/images/mb04_080317.gif" \* MERGEFORMATINET ??????9.小明要在半径为1 m、圆心角为60°的扇形铁皮中剪取一块面积尽可能大的正方形铁皮,小明在扇形铁皮上设计如图1和图2所示的甲、乙两种剪取方案,请你帮小明计算一下,按甲、乙两种方案剪取所得的正方形的面积,并估算哪个正方形的面积较大.(估算时?? INCLUDEPICTURE

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1.73,结果保留两个有效数字).?? INCLUDEPICTURE "http://video.etiantian.com/fav.gif" \* MERGEFORMATINET ??????

思路点拨:要比较甲、乙两方案剪取的正方形的面积大小,关键在于求出边长.

?? INCLUDEPICTURE "http://video.etiantian.com/security/9d6bb1eee1894ab4e402b4d8c40cdcbe/4cda95c7/ett20/resource/d4ebace7491106c9a0b23a76722235a5/jdlt.files/image070.jpg" \* MERGEFORMATINET ??????

解:方案甲:如图,连接OH,设EF=x,则OE=2OF,?? INCLUDEPICTURE "http://video.etiantian.com/security/9d6bb1eee1894ab4e402b4d8c40cdcbe/4cda95c7/ett20/resource/d4ebace7491106c9a0b23a76722235a5/jdlt.files/image071.gif" \* MERGEFORMATINET ??????,

∴ ?? INCLUDEPICTURE "http://video.etiantian.com/security/9d6bb1eee1894ab4e402b4d8c40cdcbe/4cda95c7/ett20/resource/d4ebace7491106c9a0b23a76722235a5/jdlt.files/image072.gif" \* MERGEFORMATINET ??????. 在Rt△OGH中,OH2=GH2+OG2,

即?? INCLUDEPICTURE "http://video.etiantian.com/security/9d6bb1eee1894ab4e402b4d8c40cdcbe/4cda95c7/ett20/resource/d4ebace7491106c9a0b23a76722235a5/jdlt.files/image073.gif" \* MERGEFORMATINET ??????,

解得?? INCLUDEPICTURE "http://video.etiantian.com/security/9d6bb1eee1894ab4e402b4d8c40cdcbe/4cda95c7/ett20/resource/d4ebace7491106c9a0b23a76722235a5/jdlt.files/image074.gif" \* MERGEFORMATINET ??????.

?? 方案乙:如图所示,作?? INCLUDEPICTURE

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dcbe/4cda95c7/ett20/resource/d4ebace7491106c9a0b23a76722235a5/

jdlt.files/image075.gif" \* MERGEFORMATINET ??????于M,交??

INCLUDEPICTURE

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dcbe/4cda95c7/ett20/resource/d4ebace7491106c9a0b23a76722235a5/

jdlt.files/image076.gif" \* MERGEFORMATINET ??????于N,

则M、N分别是?? INCLUDEPICTURE "http://video.etiantian.com/security/9d6bb1eee1894ab4e402b4d8c40cdcbe/4cda95c7/ett20/resource/d4ebace7491106c9a0b23a76722235a5/jdlt.files/image077.gif" \* MERGEFORMATINET ??????和?? INCLUDEPICTURE

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"http://video.etiantian.com/security/9d6bb1eee1894ab4e402b4d8c40cdcbe/4cda95c7/ett20/resource/d质量至上 精益求精

?? 成都起航教育个性化教育教案

4ebace7491106c9a0b23a76722235a5/jdlt.files/image079.gif" \* MERGEFORMATINET ??????.

设?? INCLUDEPICTURE "http://video.etiantian.com/security/9d6bb1eee1894ab4e402b4d8c40cdcbe/4cda95c7/ett20/resource/d4ebace7491106c9a0b23a76722235a5/jdlt.files/image080.gif" \* MERGEFORMATINET ??????,则?? INCLUDEPICTURE

"http://video.etiantian.com/security/9d6bb1eee1894ab4e402b4d8c40cdcbe/4cda95c7/ett20/resource/d4ebace7491106c9a0b23a76722235a5/jdlt.files/image081.gif" \* MERGEFORMATINET ??????,在?? INCLUDEPICTURE

"http://video.etiantian.com/security/9d6bb1eee1894ab4e402b4d8c40cdcbe/4cda95c7/ett20/resource/d4ebace7491106c9a0b23a76722235a5/jdlt.files/image082.gif" \* MERGEFORMATINET ??????中, ?? INCLUDEPICTURE "http://video.etiantian.com/security/9d6bb1eee1894ab4e402b4d8c40cdcbe/4cda95c7/ett20/resource/d4ebace7491106c9a0b23a76722235a5/jdlt.files/image083.gif" \* MERGEFORMATINET ??????,即?? INCLUDEPICTURE

"http://video.etiantian.com/security/9d6bb1eee1894ab4e402b4d8c40cdcbe/4cda95c7/ett20/resource/d4ebace7491106c9a0b23a76722235a5/jdlt.files/image084.gif" \* MERGEFORMATINET ??????,

∴ ?? INCLUDEPICTURE "http://video.etiantian.com/security/9d6bb1eee1894ab4e402b4d8c40cdcbe/4cda95c7/ett20/resource/d4ebace7491106c9a0b23a76722235a5/jdlt.files/image085.gif" \* MERGEFORMATINET ??????.

若取?? INCLUDEPICTURE "http://video.etiantian.com/security/9d6bb1eee1894ab4e402b4d8c40cdcbe/4cda95c7/ett20/resource/d4ebace7491106c9a0b23a76722235a5/jdlt.files/image086.gif" \* MERGEFORMATINET ??????,则?? INCLUDEPICTURE

"http://video.etiantian.com/security/9d6bb1eee1894ab4e402b4d8c40cdcbe/4cda95c7/ett20/resource/d4ebace7491106c9a0b23a76722235a5/jdlt.files/image087.gif" \* MERGEFORMATINET ??????,?? INCLUDEPICTURE

"http://video.etiantian.com/security/9d6bb1eee1894ab4e402b4d8c40cdcbe/4cda95c7/ett20/resource/d4ebace7491106c9a0b23a76722235a5/jdlt.files/image088.gif" \* MERGEFORMATINET ??????. ∴ x2>y2,即按甲方案剪得的正方形面积较大.

总结升华:此类问题是生活中的一个实际问题,解决此类问题时,应先将实际问题转化为数学问题.

?? INCLUDEPICTURE "http://video.etiantian.com/security/9d6bb1eee1894ab4e402b4d8c40cdcbe/4cda95c7/ett20/resource/d4ebace7491106c9a0b23a76722235a5/images/mb04_080317.gif" \* MERGEFORMATINET ??????10.已知射线OF交⊙O于B,半径OA⊥OB,P是射线OF上的一个动点(不与O、B重合),直线AP交⊙O于D,过D作⊙O的切线交射线OF于E.?? INCLUDEPICTURE "http://video.etiantian.com/fav.gif" \* MERGEFORMATINET ??????

(1)如图所示是点P在圆内移动时符合已知条件的图形,请你在图中画出点P在圆外移动时符合已知条

件的图形.

?? INCLUDEPICTURE "http://video.etiantian.com/security/9d6bb1eee1894ab4e402b4d8c40cdcbe/4cda95c7/ett20/resource/d4ebace7491106c9a0b23a76722235a5/jdlt.files/image089.jpg" \* MERGEFORMATINET ??????

(2)观察图形,点P在移动过程中,△DPE的边、角或形状存在某些规律,请你通过观察、测量、比较写

出一条与△DPE的边、角或形状有关的规律.

(3)点P在移动过程中,设∠DEP的度数为x,∠OAP的度数为y,求y与x的函数关系式,并写出自变量x的

取值范围.

质量至上 精益求精

?? 成都起航教育个性化教育教案

思路点拨:如图所示,连接OD,因为DE是⊙O的切线,故∠ODE=90°,又OA=OD,故∠A=∠ODA,

∠OAP+∠OPD=90°,∠ODA+∠ADC=90°,故∠OPD=∠ADC=∠EDP,△DEP是等腰三角形.

解:(1)在BF上取点P,连AP交⊙O于点D,过D作⊙O切线,交OF于E,如图即为所求.

(2)∠EDP=∠DPE,或ED=EP或△PDE是等腰三角形.

(3)根据题意,得△PDE是等腰三角形,

∴ ∠EDP=∠DPE,

∴ ?? INCLUDEPICTURE "http://video.etiantian.com/security/9d6bb1eee1894ab4e402b4d8c40cdcbe/4cda95c7/ett20/resource/d4ebace7491106c9a0b23a76722235a5/jdlt.files/image091.gif" \* MERGEFORMATINET ??????,

在Rt△OAP中,?? INCLUDEPICTURE "http://video.etiantian.com/security/9d6bb1eee1894ab4e402b4d8c40cdcbe/4cda95c7/ett20/resource/d4ebace7491106c9a0b23a76722235a5/jdlt.files/image092.gif" \* MERGEFORMATINET ??????,

∴ ?? INCLUDEPICTURE "http://video.etiantian.com/security/9d6bb1eee1894ab4e402b4d8c40cdcbe/4cda95c7/ett20/resource/d4ebace7491106c9a0b23a76722235a5/jdlt.files/image093.gif" \* MERGEFORMATINET ??????,自变量x的取值范围是?? INCLUDEPICTURE "http://video.etiantian.com/security/9d6bb1eee1894ab4e402b4d8c40cdcbe/4cda95c7/ett20/resource/d4ebace7491106c9a0b23a76722235a5/jdlt.files/image094.gif" \* MERGEFORMATINET ??????且?? INCLUDEPICTURE

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????三、课后综合习题

??三、课后综合习题

三、课后综合习题

一、选择题(每小题3分,共24分)

1.如图,把一个量角器放置在∠BAC的上面,则∠BAC的度数是( )

(A)30o.(B)60o.(C)15o.(D)20o.

?? ?? ??

(第1题) (第2题) (第3题)

2.如图,实线部分是半径为9m的两条等弧组成的游泳池.若每条圆弧所在的圆都经过另一

个圆的圆心,则游泳池的周长为( )

(A)12?? EMBED Equation.DSMT4 ??????m.(B)18?? EMBED Equation.DSMT4

??????m.(C)20?? EMBED Equation.DSMT4 ??????m.(D)24?? EMBED Equation.DSMT4 ??????m.

3.如图,P(?? EMBED Equation.DSMT4 ??????,?? EMBED Equation.DSMT4 ??????)是以坐

标原点为圆心,5为半径的圆周上的点,若?? EMBED Equation.DSMT4 ??????,?? EMBED Equation.DSMT4 ??????都是整数,则这样的点共有( )

(A)4.(B)8.(C)12.(D)16.

4.用一把带有刻度尺的直角尺,(1)可以画出两条平行的直线a和b,如图①;(2)可以画

出∠AOB的平分线OP,如图②;(3)可以检验工件的凹面是否为半圆,如图③;(4)可质量至上 精益求精

?? 成都起航教育个性化教育教案

以量出一个圆的半径,如图④.这四种说法正确的有( )

HYPERLINK "http://www.1230.org"

图① 图② 图③ 图④

(A)4个.(B)3个.(C)2个.(D)1个.

5.如图,这是中央电视台“曲苑杂谈”中的一幅图案,它是一扇形,其中∠AOB为120o,OC

长为8cm,CA长为12cm,则阴影部分的面积为( )

(A)?? EMBED Equation.DSMT4 ??????.(B)?? EMBED Equation.DSMT4 ??????.(C)

?? EMBED Equation.DSMT4 ??????.(D)?? EMBED Equation.DSMT4 ??????.

?? ?? ??

(第5题) (第6题) (第7题)

6.如图,小华从一个圆形场地的A点出发,沿着与半径OA夹角为?? EMBED Equation.DSMT4

??????的方向行走,走到场地边缘B后,再沿与半径OB夹角为?? EMBED Equation.DSMT4 ??????的方向折向行走.按照这种方式,小华第五次走到场地边缘时处于弧AB上,此时∠

(A)52o.(B)60o.(C)72o.(D)76o. AOE=56o,则?? EMBED Equation.DSMT4 ??????的度数是( )

7.小明不慎把家里的圆形玻璃打碎了,其中四块碎片如图所示,为配到与原来大小一样的圆

形玻璃,小明带到商店去的一块玻璃片应该是( )

(A)第①块.(B)第②块.(C)第③块.(D)第④块.

8.已知圆锥的底面半径为1cm,母线长为3cm,则其全面积为( )

(A)?? EMBED Equation.DSMT4 ??????.(B)?? EMBED Equation.DSMT4 ??????.(C)?? EMBED Equation.DSMT4 ??????.(D)?? EMBED Equation.DSMT4 ??????.

二、填空题(每小题3分,共18分)

9.某单位拟建的大门示意图如图所示,上部是一段直径为10米的圆弧形,下部是矩形ABCD,

其中AB=3.7米,BC=6米,则?? HYPERLINK "http://www.1230.org" ??弧AD的中点到BC的??距离是____________米.

?? ?? ??

(第9题) (第10题) (第11题)

10.如图,一宽为2cm的刻度尺在圆上移动,当刻度尺的一边与圆相切时,另一边与圆两个交

点处的读数恰好为“2”和“8”(单位:cm),则该圆的半径为_____________cm.

11.如图,∠1的正切值等于_____________.

12.一个小熊的头像如图所示.图中反映出圆与圆的四种位置关系,但是其中有一种位置关系

没有反映出来.请你写出这种位置关系,它是____________.

?? ?? ??

(第12题) (第13题) (第14题)

13.如图,U型池可以看作一个长方体去掉一个“半圆柱”而成,中间可供滑行部分的截面是

半径为4m的半圆,其边缘AB=CD=20m,点E在CD上,CE=2m,一滑板爱好者从A点滑到E点,则他滑行的最短距离约为______________m.(边缘部分的厚度忽略不计,结果保留整数)

14.三个直立于水平面上的形状完全相同的几何体(下底面为圆面,单位:cm)如图所示.则三

个几何体的体积和为 cm3.(计算结果保留?? EMBED Equation.DSMT4 ??????) 质量至上 精益求精

??

成都起航教育个性化教育教案

三、解答题(每小题6分,共18分)

15.如图,AB为⊙O直径,BC切⊙O于B,CO交⊙O交于D,AD的延长线交BC于E,若∠

C = 25°,求∠A的度数.

??

??16.如图,AB是OD的弦,半径OC、OD分别交AB于点E、F,且AE=BF,请你找出线段

OE与OF的数量关系,并给予证明.

17.如图,P为正比例函数?? EMBED Equation.3 ????图象上的一个动点,⊙P的半径为3,

??

设点P的坐标为(?? EMBED Equation.3 ??????,?? EMBED Equation.3 ??????). (1)求⊙P与直线?? EMBED Equation.3 ??????相切时点P的坐标;

?? ( 2)请直接写出⊙P与直线?? EMBED Equation.3 ??????相交、相离时?? EMBED Equation.3

??????的取值范围.

四、解答题(每小题8分,共24分)

18.从卫生纸的包装纸上得到以下资料:两层300格,每格11.4cm×11cm,如图甲.用尺量出

整卷卫生纸的半径(?? EMBED Equation.DSMT4 ??????)与纸筒内芯的半径(?? EMBED Equation.DSMT4 ??????),分别为5.8cm和2.3cm,如图乙.那么该两层卫生纸的厚度为多少cm?(π取3.14,结果精确到0.001cm)

??

图① 图②

19.如图,A是半径为12cm的⊙O上的定点,动点P从A出发,以?? EMBED Equation.DSMT4

??????cm/s的速度沿圆周逆时针运动,当点P回到A地立即停止运动.

(1)如果∠POA=90o,?? HYPERLINK "http://www.1230.org" ??求点P运动的时间??; (2)如果点B是OA延长线上的一点,AB=OA,那么当点P运动的时间为2s时,判断直

线BP与⊙O的位置关系,并说明理由.

质量至上 精益求精

?? 成都起航教育个性化教育教案

??

20.如图,已知直角坐标系中一条圆弧经过正方形网格的格点A、B、C.

(1)用直尺画出该圆弧所在圆的圆心M的位置;

(2)若A点的坐标为(0,4),D点的坐标为(7,0),试验证点D是否在经过点A、B、

C的抛物线上;

(3)在(2)的条件下,求证直线CD是⊙M的切线.

??

五、解答题(每小题8分,共16分)

21.如图,图①是一个小朋友玩“滚铁环”的游戏。铁环是圆形的,铁环向前滚动时,铁环钩

保持与铁环相切.将这个游戏抽象为数学问题,如图②.已知铁环的半径为5个单位(每个单位为5cm),设铁环中心为O,铁环钩与铁环相切点为M,铁环与地面接触点为A,∠MOA=?? EMBED Equation.DSMT4 ??????,且?? EMBED Equation.DSMT4 ??????.

(1)求点M离地面AC的高度MB(单位:厘米);

(2)设人站立点C与点A的水平距离AC等于11个单位,求铁环钩MF的长度(单位:

厘米).

??

22.图①是用钢丝制作的一个几何探究具,其中△ABC内接于⊙G,AB是⊙G的直径,AB=6,

AC=3.现将制作的几何探究工具放在平面直角坐标系中(如图②),然后点A在射线OX由点O开始向右滑动,点B在射线OY上也随之向点O滑动(如图③),当点B滑动至与点O重合时运动结束.

(1)试说明在运动过程中,原点O始终在⊙G上;

(2)设点C的坐标为(?? EMBED Equation.DSMT4 ??????,?? EMBED Equation.DSMT4

??????),试求?? EMBED Equation.DSMT4 ??????与?? EMBED Equation.DSMT4 ??????之间的函?? HYPERLINK "http://www.1230.org" ????,并写出自变量??

EMBED Equation.DSMT4 ??????的取值范围;

(3)在整个运动过程中,点C运动的路程是多少?

??

图① 图② 图③

参考答案

B 组

一、选择题

质量至上 精益求精

?? 成都起航教育个性化教育教案

1.C 2.D 3.C 4.A 5.B 6.A 7.B 8.C

二、填空题

9.4.7 10.5 11.?? EMBED Equation.DSMT4 ???? 12.相交 13.22 14.60?? EMBED

??

Equation.DSMT4 ??????

三、解答题

15.∵AB为⊙O的直径,BC切⊙O于B,∴∠ABC = 90°,∵∠C = 25°,∴∠BOC = 65o,∵∠A = ?? EMBED Equation.3 ????∠BOD,∴∠A = 32.5o. 16.解:OE=OF.证明:作OM

??

⊥AM,垂足为M.根据垂径定理得AM=BM.∵AE=BF,∴AM-AE=BM-BF,即EM=FM.∴OE=OF. 17.(1)当⊙P与直线?? EMBED Equation.DSMT4 ??????相切时,点P的坐标为(5,?? EMBED Equation.DSMT4 ????)或(?? EMBED Equation.DSMT4 ??????,?? EMBED

??

Equation.DSMT4 ????);(2)当?? EMBED Equation.DSMT4 ??????时,⊙P与直线?? EMBED

??

Equation.DSMT4 ??????相交.当?? EMBED Equation.DSMT4 ??????或?? EMBED Equation.DSMT4 ??????时,⊙P与直线?? EMBED Equation.DSMT4 ??????相离.

四、解答题

18.设该两层卫生纸的厚度为xm,则:?? EMBED Equation.DSMT4 ???? ,解得?? EMBED ??

Equation.DSMT4 ??????,答:设两层卫生纸的厚度约为0.026cm. 19.(1)3s;(2)当点P运动2s时,∠POA=60o,∴OA=AP=AB,∴∠OPB=90o,∴BP与⊙O相切. 20.(1)略;

(2)?? EMBED Equation.DSMT4 ????,点D不在抛物线上;(3)略.

??

五、解答题

21.(1)过M作与AC平行的直线,与OA、FC分别相交于H、N.易求得铁环钩离地面的高度MB为1cm;(2)解Rt△FMN,结合勾股定理与三角函数可得,铁环钩的长度FM为50/3cm.

22.(1)连OG,OG=AG=BG,∴点O始终在⊙G上;(2)作CD⊥?? EMBED Equation.DSMT4 ??????轴,CE⊥?? EMBED Equation.DSMT4 ??????轴垂足分别为D,E,可得△CAD∽△CBE,得?? EMBED Equation.DSMT4 ????,?? EMBED Equation.DSMT4 ????;(3)线段的两个端

????

点分别为C1(?? EMBED Equation.DSMT4 ????,?? EMBED Equation.DSMT4 ????),C2(??

????

EMBED Equation.DSMT4 ??????,3),当OA?? EMBED Equation.DSMT4 ??????时,C1(?? HYPERLINK "http://www.1230.org" ???? EMBED Equation.DSMT4 ??????,?? EMBED

??

Equation.DSMT4 ????);当OA?? EMBED Equation.DSMT4 ??????时,C3(?? EMBED

??

Equation.DSMT4 ????,?? EMBED Equation.DSMT4 ????);C1C2=3,C2C3=3?? EMBED

????

Equation.DSMT4 ??????,点C运动的路程为?? EMBED Equation.DSMT4 ??????

三、学生对于本次课的评价:

三、学生对于本次课的评价:

三、学生对于本次课的评价:

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