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第二十八章　圆
28.2 过三点的圆
INCLUDEPICTURE"复习回顾.tif" INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\复习回顾.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\复习回顾.tif" \* MERGEFORMATINET
1．已知A，B，C三点，若过其中任意两点画一条直线，则画出的不同直线(　　)
A．一定有三条 B．只能有一条
C．可能有三条，也可能只有一条 D．以上结论都不对
2．线段BC上有3个点P1，P2，P3(不与点B，C重合)，直线BC外有一点A，把A分别和B，P1，P2，P3，C中的任意两点连接起来，可以得到的三角形个数为(　　)
A．8 B．10 C．12 D．20
3．已知⊙O的半径为2，则⊙O中最长的弦长为(　　)
A．2 B. C．4 D.
INCLUDEPICTURE"预习效果检测.tif" INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\预习效果检测.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\预习效果检测.tif" \* MERGEFORMATINET
1．不在____________的三点确定一个圆．
2．我们把经过三角形三个________的圆叫做三角形的外接圆，外接圆的________叫做三角形的外心．
3．[2023邢台期中]如图，点A，B，C，D均在直线l上，点P在直线l外，则经过其中任意三个点，最多可画出圆的个数为(　　)
A．12 B．8 C．6 D．4
INCLUDEPICTURE"册87.tif" INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\册87.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\册87.tif" \* MERGEFORMATINET (第3题)　　INCLUDEPICTURE"册88.tif" INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\册88.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\册88.tif" \* MERGEFORMATINET (第4题)
4．如图，AC，BE是⊙O的直径，弦AD与BE交于点F，连接AB，AE，DE，CF，下列三角形中，外心是点O的是(　　)
A．△ABF B．△ACF C．△ADE D．△AEF
5．[2023绍兴月考]如图，在单位长度为1的正方形网格图中，一条圆弧经过A(0，4)，B(4，4)，C(6，2)三个格点，请在网格中进行下列操作：
INCLUDEPICTURE"册89.tif" INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\册89.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\册89.tif" \* MERGEFORMATINET
(1)在图中确定该圆弧所在圆的圆心D点的位置；
(2)D点的坐标为________，求⊙D的半径长．
INCLUDEPICTURE"课堂导学.tif" INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\课堂导学.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\课堂导学.tif" \* MERGEFORMATINET
INCLUDEPICTURE"W21.tif" INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\W21.tif" \* MERGEFORMATINET
知识点1 过三点的圆INCLUDEPICTURE"L1.tif" INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\L1.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\L1.tif" \* MERGEFORMATINET 平面直角坐标系内的三个点A(4，－3)，B(0，－3)，C(2，－3)，________确定一个圆(填“能”或“不能”)．
变式1下列条件中能够确定一个圆的是(　　)
A．已知圆心
B．已知半径
C．已知三个点
D．过一个三角形的三个顶点
　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　知识点2 三角形的外接圆
INCLUDEPICTURE"L2.tif" INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\L2.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\L2.tif" \* MERGEFORMATINET [2023平凉期中]如图，在Rt△ABC中，∠C＝90°.
(1)求作：△ABC的外接圆⊙O(不写作法，保留作图痕迹)；
(2)若AC＝6 cm，BC＝8 cm，求⊙O的面积．
INCLUDEPICTURE"册90.tif" INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\册90.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\册90.tif" \* MERGEFORMATINET
　　　　　　　　　　　　　　　
变式2－1如图，△ABC的三个顶点的坐标分别为A(－1，3)，B(－2，－2)，C(4，－2)，则△ABC的外接圆圆心的坐标为______．
INCLUDEPICTURE"册91.tif" INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\册91.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\册91.tif" \* MERGEFORMATINET
变式2－2小明家的房前有一块矩形的空地，空地上有三棵树A，B，C，如图，小明想建一个圆形花坛，使三棵树都在花坛的边上．请你帮小明把花坛的位置画出来．(不写作法，保留作图痕迹)
INCLUDEPICTURE"册92.tif" INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\册92.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\册92.tif" \* MERGEFORMATINET
第二十八章　圆
28.2 过三点的圆
INCLUDEPICTURE"复习回顾.tif" INCLUDEPICTURE "复习回顾.tif" \* MERGEFORMAT INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\复习回顾.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\复习回顾.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\复习回顾.tif" \* MERGEFORMATINET
1．C　2.B　3.C
INCLUDEPICTURE"预习效果.tif" INCLUDEPICTURE "预习效果.tif" \* MERGEFORMAT INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\预习效果.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\预习效果.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\预习效果.tif" \* MERGEFORMATINET
1．同一直线上　2.顶点；圆心　3.C　4.C
5．解：(1)该圆弧所在圆的圆心D点的位置如图所示．
INCLUDEPICTURE"答104.tif" INCLUDEPICTURE "答104.tif" \* MERGEFORMAT INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\答104.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\答104.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\答104.tif" \* MERGEFORMATINET
(2)(2，0)
如图，连接DC，由勾股定理得DC＝＝2 .
∴⊙D的半径长为2 .
INCLUDEPICTURE"课堂导学.tif" INCLUDEPICTURE "课堂导学.tif" \* MERGEFORMAT INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\课堂导学.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\课堂导学.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\课堂导学.tif" \* MERGEFORMATINET
例1　不能　变式1.D
例2　解：(1)如图所示，⊙O即为所求．
INCLUDEPICTURE"答105.tif" INCLUDEPICTURE "答105.tif" \* MERGEFORMAT INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\答105.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\答105.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\答105.tif" \* MERGEFORMATINET
(2)∵∠C＝90°，AC＝6 cm，BC＝8 cm，
∴根据勾股定理，得AB＝＝10 cm，
∴OA＝AB＝5 cm，∴⊙O的面积为π×52＝25π(cm2)．
变式2－1.(1，0)
变式2－2.如图所示，⊙O即为所求．
INCLUDEPICTURE"加图贴纸.tif" INCLUDEPICTURE "加图贴纸.tif" \* MERGEFORMAT INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\加图贴纸.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\加图贴纸.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\加图贴纸.tif" \* MERGEFORMATINET

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