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第二十八章　圓
28.2 過三點的圓
INCLUDEPICTURE"復習回顧.tif" INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\復習回顧.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\復習回顧.tif" \* MERGEFORMATINET
1．已知A，B，C三點，若過其中任意兩點畫一條直線，則畫出的不同直線(　　)
A．一定有三條 B．只能有一條
C．可能有三條，也可能只有一條 D．以上結論都不對
2．線段BC上有3個點P1，P2，P3(不與點B，C重合)，直線BC外有一點A，把A分別和B，P1，P2，P3，C中的任意兩點連接起來，可以得到的三角形個數為(　　)
A．8 B．10 C．12 D．20
3．已知⊙O的半徑為2，則⊙O中最長的弦長為(　　)
A．2 B. C．4 D.
INCLUDEPICTURE"預習效果檢測.tif" INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\預習效果檢測.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\預習效果檢測.tif" \* MERGEFORMATINET
1．不在____________的三點確定一個圓．
2．我們把經過三角形三個________的圓叫做三角形的外接圓，外接圓的________叫做三角形的外心．
3．[2023邢臺期中]如圖，點A，B，C，D均在直線l上，點P在直線l外，則經過其中任意三個點，最多可畫出圓的個數為(　　)
A．12 B．8 C．6 D．4
INCLUDEPICTURE"冊87.tif" INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\冊87.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\冊87.tif" \* MERGEFORMATINET (第3題)　　INCLUDEPICTURE"冊88.tif" INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\冊88.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\冊88.tif" \* MERGEFORMATINET (第4題)
4．如圖，AC，BE是⊙O的直徑，弦AD與BE交于點F，連接AB，AE，DE，CF，下列三角形中，外心是點O的是(　　)
A．△ABF B．△ACF C．△ADE D．△AEF
5．[2023紹興月考]如圖，在單位長度為1的正方形網格圖中，一條圓弧經過A(0，4)，B(4，4)，C(6，2)三個格點，請在網格中進行下列操作：
INCLUDEPICTURE"冊89.tif" INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\冊89.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\冊89.tif" \* MERGEFORMATINET
(1)在圖中確定該圓弧所在圓的圓心D點的位置；
(2)D點的坐標為________，求⊙D的半徑長．
INCLUDEPICTURE"課堂導學.tif" INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\課堂導學.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\課堂導學.tif" \* MERGEFORMATINET
INCLUDEPICTURE"W21.tif" INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\W21.tif" \* MERGEFORMATINET
知識點1 過三點的圓INCLUDEPICTURE"L1.tif" INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\L1.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\L1.tif" \* MERGEFORMATINET 平面直角坐標系內的三個點A(4，－3)，B(0，－3)，C(2，－3)，________確定一個圓(填“能”或“不能”)．
變式1下列條件中能夠確定一個圓的是(　　)
A．已知圓心
B．已知半徑
C．已知三個點
D．過一個三角形的三個頂點
　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　知識點2 三角形的外接圓
INCLUDEPICTURE"L2.tif" INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\L2.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\L2.tif" \* MERGEFORMATINET [2023平涼期中]如圖，在Rt△ABC中，∠C＝90°.
(1)求作：△ABC的外接圓⊙O(不寫作法，保留作圖痕跡)；
(2)若AC＝6 cm，BC＝8 cm，求⊙O的面積．
INCLUDEPICTURE"冊90.tif" INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\冊90.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\冊90.tif" \* MERGEFORMATINET
　　　　　　　　　　　　　　　
變式2－1如圖，△ABC的三個頂點的坐標分別為A(－1，3)，B(－2，－2)，C(4，－2)，則△ABC的外接圓圓心的坐標為______．
INCLUDEPICTURE"冊91.tif" INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\冊91.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\冊91.tif" \* MERGEFORMATINET
變式2－2小明家的房前有一塊矩形的空地，空地上有三棵樹A，B，C，如圖，小明想建一個圓形花壇，使三棵樹都在花壇的邊上．請你幫小明把花壇的位置畫出來．(不寫作法，保留作圖痕跡)
INCLUDEPICTURE"冊92.tif" INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\冊92.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\冊92.tif" \* MERGEFORMATINET
第二十八章　圓
28.2 過三點的圓
INCLUDEPICTURE"復習回顧.tif" INCLUDEPICTURE "復習回顧.tif" \* MERGEFORMAT INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\復習回顧.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\復習回顧.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\復習回顧.tif" \* MERGEFORMATINET
1．C　2.B　3.C
INCLUDEPICTURE"預習效果.tif" INCLUDEPICTURE "預習效果.tif" \* MERGEFORMAT INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\預習效果.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\預習效果.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\預習效果.tif" \* MERGEFORMATINET
1．同一直線上　2.頂點；圓心　3.C　4.C
5．解：(1)該圓弧所在圓的圓心D點的位置如圖所示．
INCLUDEPICTURE"答104.tif" INCLUDEPICTURE "答104.tif" \* MERGEFORMAT INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\答104.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\答104.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\答104.tif" \* MERGEFORMATINET
(2)(2，0)
如圖，連接DC，由勾股定理得DC＝＝2 .
∴⊙D的半徑長為2 .
INCLUDEPICTURE"課堂導學.tif" INCLUDEPICTURE "課堂導學.tif" \* MERGEFORMAT INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\課堂導學.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\課堂導學.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\課堂導學.tif" \* MERGEFORMATINET
例1　不能　變式1.D
例2　解：(1)如圖所示，⊙O即為所求．
INCLUDEPICTURE"答105.tif" INCLUDEPICTURE "答105.tif" \* MERGEFORMAT INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\答105.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\答105.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\答105.tif" \* MERGEFORMATINET
(2)∵∠C＝90°，AC＝6 cm，BC＝8 cm，
∴根據勾股定理，得AB＝＝10 cm，
∴OA＝AB＝5 cm，∴⊙O的面積為π×52＝25π(cm2)．
變式2－1.(1，0)
變式2－2.如圖所示，⊙O即為所求．
INCLUDEPICTURE"加圖貼紙.tif" INCLUDEPICTURE "加圖貼紙.tif" \* MERGEFORMAT INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\加圖貼紙.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\加圖貼紙.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\加圖貼紙.tif" \* MERGEFORMATINET

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