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1、OFABCDEFEDCBOACEBODFA圆 综合练习题一、与圆有关的中档题：与圆有关的证明（证切线为主）和计算（线段长、面积、三角函数值、最值等）1.如图，BD为O的直径，AC为弦，ABAC，AD交BC于E，2AE，4ED（1）求证：ABEADB，并求AB的长；（2）延长DB到F，使BFBO，连接FA，判断直线FA与O的位置关系，并说明理由.2.已知：如图，以等边三角形ABC一边AB为直径的O与边AC、BC分别交于点D、E，过点D作DFBC，垂足为F（1）求证：DF为O的切线；（2）若等边三角形ABC的边长为4，求DF的长；（3）求图中阴影部分的面积3、如图，已知圆O 的直径AB垂直于弦CD
2、于点E，连接CO并延长交AD于点F，且CFAD（1）请证明：E是OB的中点；（2）若8AB，求CD的长4如图，AB是O的直径，点C在O上，BAC=60，P是OB上一点，过P作AB的垂线与AC的延长线交于点Q，连结OC，过点C作OCCD交PQ于点D（1）求证：CDQ是等腰三角形；（2）如果CDQCOB，求BP:PO的值5 已知:如图,BD是半圆O的直径,A是BD延长线上的一点，BCAE，交AE的延长线于点C,交半圆O于点 E，且E为DF的中点.（1）求证：AC是半圆O的切线；（2）若66 2ADAE，求BC的长ABCDEOGF6.如图，ABC内接于 O，过点A的直线交O 于点P，交BC的延长线于
3、点D，且AB2=AP AD（1）求证：ABAC；（2）如果60ABC，O的半径为 1，且 P为弧 AC的中点，求 AD的长.7如图，在ABC中，C=90,AD是BAC的平分线，O是AB上一点,以OA为半径的O经过点D.（1）求证：BC是O切线；（2）若BD=5,DC=3,求AC的长.8如图，AB是O的直径，CD是O的一条弦，且CD AB于 E，连结 AC、OC、BC.（1）求证：ACO=BCD；（2）若 BE=2，CD=8，求 AB和 AC的长.9如图，已知BC为O的直径，点A、F在O上，BCAD，垂足为D，BF交AD于E，且BEAE（1）求证：AFAB；（2）如果53sinFBC，54AB，
4、求AD的长10如图，已知直径与等边ABC的高相等的圆O分别与边AB、BC相切于点D、E，边 AC过圆心 O与圆 O相交于点F、G。（1）求证：DEAC；（2）若ABC的边长为a，求ECG的面积.11如图，在ABC中，BCA=90，以BC为直径的O交AB于点P，Q是AC的中点OPDCBAOACDB文档编码:CY6P6Z7Q5K4 HH3S1E3N3W7 ZA8E4R6N8P2文档编码:CY6P6Z7Q5K4 HH3S1E3N3W7 ZA8E4R6N8P2文档编码:CY6P6Z7Q5K4 HH3S1E3N3W7 ZA8E4R6N8P2文档编码:CY6P6Z7Q5K4 HH3S1E3N3W7 ZA8
5、E4R6N8P2文档编码:CY6P6Z7Q5K4 HH3S1E3N3W7 ZA8E4R6N8P2文档编码:CY6P6Z7Q5K4 HH3S1E3N3W7 ZA8E4R6N8P2文档编码:CY6P6Z7Q5K4 HH3S1E3N3W7 ZA8E4R6N8P2文档编码:CY6P6Z7Q5K4 HH3S1E3N3W7 ZA8E4R6N8P2文档编码:CY6P6Z7Q5K4 HH3S1E3N3W7 ZA8E4R6N8P2文档编码:CY6P6Z7Q5K4 HH3S1E3N3W7 ZA8E4R6N8P2文档编码:CY6P6Z7Q5K4 HH3S1E3N3W7 ZA8E4R6N8P2文档编码:CY6P6Z7
6、Q5K4 HH3S1E3N3W7 ZA8E4R6N8P2文档编码:CY6P6Z7Q5K4 HH3S1E3N3W7 ZA8E4R6N8P2文档编码:CY6P6Z7Q5K4 HH3S1E3N3W7 ZA8E4R6N8P2文档编码:CY6P6Z7Q5K4 HH3S1E3N3W7 ZA8E4R6N8P2文档编码:CY6P6Z7Q5K4 HH3S1E3N3W7 ZA8E4R6N8P2文档编码:CY6P6Z7Q5K4 HH3S1E3N3W7 ZA8E4R6N8P2文档编码:CY6P6Z7Q5K4 HH3S1E3N3W7 ZA8E4R6N8P2文档编码:CY6P6Z7Q5K4 HH3S1E3N3W7 ZA8
7、E4R6N8P2文档编码:CY6P6Z7Q5K4 HH3S1E3N3W7 ZA8E4R6N8P2文档编码:CY6P6Z7Q5K4 HH3S1E3N3W7 ZA8E4R6N8P2文档编码:CY6P6Z7Q5K4 HH3S1E3N3W7 ZA8E4R6N8P2文档编码:CY6P6Z7Q5K4 HH3S1E3N3W7 ZA8E4R6N8P2文档编码:CY6P6Z7Q5K4 HH3S1E3N3W7 ZA8E4R6N8P2文档编码:CY6P6Z7Q5K4 HH3S1E3N3W7 ZA8E4R6N8P2文档编码:CY6P6Z7Q5K4 HH3S1E3N3W7 ZA8E4R6N8P2文档编码:CY6P6Z7
8、Q5K4 HH3S1E3N3W7 ZA8E4R6N8P2文档编码:CY6P6Z7Q5K4 HH3S1E3N3W7 ZA8E4R6N8P2文档编码:CY6P6Z7Q5K4 HH3S1E3N3W7 ZA8E4R6N8P2文档编码:CY6P6Z7Q5K4 HH3S1E3N3W7 ZA8E4R6N8P2文档编码:CY6P6Z7Q5K4 HH3S1E3N3W7 ZA8E4R6N8P2文档编码:CY6P6Z7Q5K4 HH3S1E3N3W7 ZA8E4R6N8P2文档编码:CY6P6Z7Q5K4 HH3S1E3N3W7 ZA8E4R6N8P2文档编码:CY6P6Z7Q5K4 HH3S1E3N3W7 ZA8
9、E4R6N8P2文档编码:CY6P6Z7Q5K4 HH3S1E3N3W7 ZA8E4R6N8P2文档编码:CY6P6Z7Q5K4 HH3S1E3N3W7 ZA8E4R6N8P2文档编码:CY6P6Z7Q5K4 HH3S1E3N3W7 ZA8E4R6N8P2文档编码:CY6P6Z7Q5K4 HH3S1E3N3W7 ZA8E4R6N8P2文档编码:CY6P6Z7Q5K4 HH3S1E3N3W7 ZA8E4R6N8P2文档编码:CY6P6Z7Q5K4 HH3S1E3N3W7 ZA8E4R6N8P2文档编码:CY6P6Z7Q5K4 HH3S1E3N3W7 ZA8E4R6N8P2文档编码:CY6P6Z7
10、Q5K4 HH3S1E3N3W7 ZA8E4R6N8P2文档编码:CY6P6Z7Q5K4 HH3S1E3N3W7 ZA8E4R6N8P2文档编码:CY6P6Z7Q5K4 HH3S1E3N3W7 ZA8E4R6N8P2文档编码:CY6P6Z7Q5K4 HH3S1E3N3W7 ZA8E4R6N8P2文档编码:CY6P6Z7Q5K4 HH3S1E3N3W7 ZA8E4R6N8P2文档编码:CY6P6Z7Q5K4 HH3S1E3N3W7 ZA8E4R6N8P2文档编码:CY6P6Z7Q5K4 HH3S1E3N3W7 ZA8E4R6N8P2OQPCBAGFEDCOBA第 13 题图（1）请你判断直线PQ
11、与O的位置关系，并说明理由；（2）若A30，AP=2 3，求O半径的长.12如图，已知点A是O上一点，直线MN过点A，点B是MN上的另一点，点C是OB的中点，12ACOB，若点P是O上的一个动点,且30OBA,AB=2 3时，求APC的面积的最大值13如图，等腰ABC中，AB=AC=13，BC=10，以AC为直径作O交BC于点D，交AB于点G，过点D作O的切线交AB于点E，交AC的延长线与点F.（1）求证：EFAB；（2）求cosF的值.14（应用性问题）已知：如图，为了测量一种圆形零件的精度，在加工流水线上设计了用两块大小相同，且含有30的直角三角尺按图示的方式测量.(1)若O分别与AE、A
12、F交于点B、C，且AB=AC,若O与AF相切.求证:O与AE相切；(2)在满足(1)的情况下，当、分别为AE、AF的三分之一点时，且AF=3，求BC的弧长.二、圆与相似综合15已知：如图，O的内接ABC中，BAC=45，ABC=15，ADOC并交 BC的延长线于D，OC交 AB于 E.（1）求 D的度数；（2）求证：2ACAD CE；（3）求BCCD的值.16如图，O的直径为AB，过半径OA的中点G作弦ABCE，ABCMNOPFABCDEGO文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9
13、V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W
14、6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:
15、CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L
16、10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6
17、 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2
18、P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2
19、 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6EB在 BC上取一点D，分别作直线EDCD、，交直线AB于点MF、.求COA和FDM的度数；求证：FDMCOM；如图，若将垂足G改取为半径OB上任意一点，点D改取在上，仍作直线EDCD、，分别交直线AB于点MF、.试判断：此时是否仍有FDMCOM成立？若成立请证明你的结论；若不成立，请说明理由。三、圆与三角函数综合17已
20、知 O过点 D（4，3），点 H与点 D关于y轴对称，过 H作 O的切线交y轴于点 A（如图 1）。求O 半径；求sinHAO的值；如图 2，设O 与y轴正半轴交点P，点 E、F 是线段 OP上的动点（与 P点不重合），联结并延长DE、DF交O于点 B、C，直线 BC交y轴于点 G，若DEF是以 EF为底的等腰三角形，试探索sinCGO的大小怎样变化？请说明理由。四、圆与二次函数（或坐标系）综合18、如图，M的圆心在x轴上，与坐标轴交于A（0，3）、B（1，0），抛物线233yxbxc经过 A、B两点（1）求抛物线的函数解析式；（2）设抛物线的顶点为P 试判断点P与 M 的位置关系，并说明理由
21、；（3）若 M与y轴的另一交点为D，则由线段PA、线段 PD及弧 ABD围成的封闭图形PABD的面积是多少？图 1 图 2 OxyD(4,3)AHCFEPBGOxyD(4,3)图 1 图 2 文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V
22、4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6
23、文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:C
24、M9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L1
25、0U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6
26、HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P
27、1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2
28、ZY6R9V4F10W619如图，在平面直角坐标系中，O是原点，以点C（1，1）为圆心，2 为半径作圆，交x轴于A，B两点，开口向下的抛物线经过点A，B，且其顶点P在C上（1）求ACB的大小；（2）写出A，B两点的坐标；（3）试确定此抛物线的解析式；（4）在该抛物线上是否存在一点D，使线段OP与CD互相平分？若存在，求出点D的坐标；若不存在，请说明理由20（以圆为幌子，二次函数为主的代几综合题）如图，半径为 1 的1O与x轴交于AB、两点，圆心1O的坐标为(20)，二次函数2yxbxc的图象经过AB、两点，其顶点为F（1）求bc，的值及二次函数顶点F的坐标；（2）将二次函数2yxbxc的图象先
29、向下平移1 个单位，再向左平移2 个单位，设平移后图象的顶点为C，在经过点B和点0,3D的直线l上是否存在一点P，使PAC的周长最小，若存在，求出点P的坐标；若不存在，请说明理由.五、以圆为背景的探究性问题21下图中,图(1)是一个扇形OAB，将其作如下划分：第一次划分：如图(2)所示，以OA的一半 OA1的长为半径画弧交OA于点 A1，交 OB于点 B1，再作 AOB的平分线，交AB于点 C，交11AB于点 C1，得到扇形的总数为6 个，分别为：扇形 OAB、扇形 OAC、扇形 OCB、扇形 OA1B1、扇形 OA1C1、扇形 OC1B1；第二次划分：如图(3)所示，在扇形OC1B1中，按上
30、述划分方式继续划分，即以OC1的一半 OA2的长为半径画弧交OC1于点 A2，交 OB1于点 B2，再作 B1OC1的平分线，交11BC于点 D1，交22A B于点 D2，可以得到扇形的总数为11 个；第三次划分：如图(4)所示，按上述划分方式继续划分；依次划分下去.xyABO-245-1-32-1-21O1文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 H
31、K7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1
32、C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 Z
33、Y6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4
34、F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文
35、档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM
36、9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10
37、U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6(1)根据题意,完成右边的表格；(2)根据右边的表格,请你判断按上述划分方式,能否得到扇形的总数为2008个?为什么?(3)若图(1)中的扇形的圆心角AOB=m，且扇形的半径OA的长为 R我们把图(2)第一次划分的图形中，扇形11OAC（或扇形11OC B）称为第一次划分的最小扇形，其面积记为S1；把图(3)第二次划分的最小扇形面积记为S2；，把第 n 次划分的最小扇形面积记为 Sn.求1nnSS的值.22圆心角定理是“圆心角的度数与它所对的弧的度数相等
38、”，记作AOBAB（如图）；圆心角定理也可以叙述成“圆心角度数等与它所对的弧及圆心角的对顶角所对的弧的和的一半”，记作1()2AOBABCD（如图）请回答下列问题：（1）如图，猜测APBAB CD与、有怎样的等量关系,并说明理由；（2）如图，猜测APBAB CD与、有怎样的等量关系,并说明理由.（提示：“两条平行弦所夹的弧相等”可当定理用）23已知：半径为R的O经过半径为r 的O圆心，O与 O交于 M、N两点（1）如图 1，连接OO交O于点 C，过点 C作O的切线交O于点 A、B，求OAOB的值；（2）若点 C为O上一动点.当点 C运动到O内时，如图2，过点 C作O的切线交O于 A、B两点请你
39、探索OA OB的值与（1）中的结论相比较有无变化？并说明你的理由；当点运动到O外时，过点C作O的切线，若能交O于 A、B两点请你在图3中画出符合题意的图形，并探索OA OB的值（只写出OA OB的值，不必证明）POACDB图OBDAC图图CDOPAB文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM
40、9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10
41、U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 H
42、K7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1
43、C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 Z
44、Y6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4
45、F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文
46、档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6OFABCDE北京市丰台区 2015-2016 学年度第一学期初三数学第 24章 圆 综合练习题一、与圆有关的中档题：与圆有关的证明（证切线为主）和计算（线段长、面积、三角函数值、最值等）1.如图，BD为O的直径，AC为弦，ABAC，AD交BC于E，2AE，4ED（1）求证：ABEADB，并求AB的长；（2）延长DB到F，使BFBO，连接FA，判断直线FA与O的位置关系，并说明理由.1解：ABAC，ABCC.CD，ABCD又BAEDAB，ABEADBA BA EA DA B224212ABAD AEAEEDAE2
47、 3AB（舍负）（2）直线FA与O相切连接OABD为O的直径，90BAD在Rt ABD中，由勾股定理，得2221224484 3BDABAD114 32 322BFBOBD2 3AB，BFBOABDFEBCOA文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7
48、M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6
49、R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F1
50、0W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编码:CM9G8L10U7M6 HK7Z2P1C7M2 ZY6R9V4F10W6文档编