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第二十八章　圓
28.4 垂徑定理*
INCLUDEPICTURE"復(fù)習(xí)回顧.tif" INCLUDEPICTURE "D:\\課件\\九數(shù)JJ河北（北京）\\復(fù)習(xí)回顧.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數(shù)JJ河北（北京）\\復(fù)習(xí)回顧.tif" \* MERGEFORMATINET
1．已知在圓內(nèi)接四邊形ABCD中，∠A∶∠B∶∠C＝9∶8∶3，則∠D的度數(shù)為(　　)
A．15° B．120° C．30° D．60°
2．如圖，AB為⊙O的直徑，D為⊙O上一點(diǎn)，若∠CAB＝36°，則∠ADC的大小是________．
INCLUDEPICTURE"冊(cè)124.tif" INCLUDEPICTURE "D:\\課件\\九數(shù)JJ河北（北京）\\冊(cè)124.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數(shù)JJ河北（北京）\\冊(cè)124.tif" \* MERGEFORMATINET (第2題)　　　　　INCLUDEPICTURE"冊(cè)125.tif" INCLUDEPICTURE "D:\\課件\\九數(shù)JJ河北（北京）\\冊(cè)125.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數(shù)JJ河北（北京）\\冊(cè)125.tif" \* MERGEFORMATINET (第3題)
3．[2023安慶期中]如圖，在△ABC中，∠C＝90°，AC＝9，AB的垂直平分線EF交AC于點(diǎn)D，交AB于點(diǎn)E，連接BD，若BD＝5，則DE的長(zhǎng)是________．
INCLUDEPICTURE"預(yù)習(xí)效果檢測(cè).tif" INCLUDEPICTURE "D:\\課件\\九數(shù)JJ河北（北京）\\預(yù)習(xí)效果檢測(cè).tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數(shù)JJ河北（北京）\\預(yù)習(xí)效果檢測(cè).tif" \* MERGEFORMATINET
1．垂直于弦的直徑________這條弦，并且________這條弦所對(duì)的兩條弧．
2．[2023嘉興期中]如圖，在⊙O中，AB是直徑，CD是弦，AB⊥CD，垂足為E，連接CO，AD，∠BAD＝20°，則下列選項(xiàng)中錯(cuò)誤的是(　　)
A．∠BOC＝2∠BAD B．BE＝EO
C．∠OCE＝50° D．CE＝DE
INCLUDEPICTURE"冊(cè)126.tif" INCLUDEPICTURE "D:\\課件\\九數(shù)JJ河北（北京）\\冊(cè)126.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數(shù)JJ河北（北京）\\冊(cè)126.tif" \* MERGEFORMATINET (第2題)　　　　　INCLUDEPICTURE"冊(cè)127.tif" INCLUDEPICTURE "D:\\課件\\九數(shù)JJ河北（北京）\\冊(cè)127.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數(shù)JJ河北（北京）\\冊(cè)127.tif" \* MERGEFORMATINET (第3題)
3．[2023福州期中]紹興市是著名的橋鄉(xiāng)，如圖，石拱橋的拱頂?shù)剿娴木嚯xCD為8 m，橋拱半徑OC＝5 m，則水面寬AB為_(kāi)_______m.
4．如圖，AB是⊙O的直徑，弦CD⊥AB于點(diǎn)E，若OE＝3，CD＝8.求⊙O的半徑．
INCLUDEPICTURE"冊(cè)128.tif" INCLUDEPICTURE "D:\\課件\\九數(shù)JJ河北（北京）\\冊(cè)128.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數(shù)JJ河北（北京）\\冊(cè)128.tif" \* MERGEFORMATINET
INCLUDEPICTURE"課堂導(dǎo)學(xué).tif" INCLUDEPICTURE "D:\\課件\\九數(shù)JJ河北（北京）\\課堂導(dǎo)學(xué).tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數(shù)JJ河北（北京）\\課堂導(dǎo)學(xué).tif" \* MERGEFORMATINET
INCLUDEPICTURE"W21.tif" INCLUDEPICTURE "D:\\課件\\九數(shù)JJ河北（北京）\\W21.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數(shù)JJ河北（北京）\\W21.tif" \* MERGEFORMATINET
知識(shí)點(diǎn)1 垂徑定理
INCLUDEPICTURE"L1.tif" INCLUDEPICTURE "D:\\課件\\九數(shù)JJ河北（北京）\\L1.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數(shù)JJ河北（北京）\\L1.tif" \* MERGEFORMATINET 如圖，⊙O的半徑為5，弦AB＝8，OC⊥AB，垂足為點(diǎn)P，則CP的長(zhǎng)等于(　　)
INCLUDEPICTURE"冊(cè)129.tif" INCLUDEPICTURE "D:\\課件\\九數(shù)JJ河北（北京）\\冊(cè)129.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數(shù)JJ河北（北京）\\冊(cè)129.tif" \* MERGEFORMATINET
A．2 B．2.5 C．3 D．4
變式1－1如圖，AB是⊙O的弦，OD⊥AB于點(diǎn)D，延長(zhǎng)OD交⊙O于點(diǎn)E，C為上一點(diǎn)，則下列說(shuō)法錯(cuò)誤的是(　　)
INCLUDEPICTURE"冊(cè)130.tif" INCLUDEPICTURE "D:\\課件\\九數(shù)JJ河北（北京）\\冊(cè)130.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數(shù)JJ河北（北京）\\冊(cè)130.tif" \* MERGEFORMATINET
A．AD＝BD B．∠ACB＝∠AOE
C.＝ D．OD＝DE
變式1－2如圖，AB為⊙O的直徑，AE為⊙O的弦，C為優(yōu)弧ABE的中點(diǎn)，CD⊥AB，垂足為D.若AE＝8，DB＝2，則⊙O的半徑為(　　)
INCLUDEPICTURE"冊(cè)131.tif" INCLUDEPICTURE "D:\\課件\\九數(shù)JJ河北（北京）\\冊(cè)131.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數(shù)JJ河北（北京）\\冊(cè)131.tif" \* MERGEFORMATINET
A．6 B．5 C．4 D．4
　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　
知識(shí)點(diǎn)2 垂徑定理的應(yīng)用
INCLUDEPICTURE"L2.tif" INCLUDEPICTURE "D:\\課件\\九數(shù)JJ河北（北京）\\L2.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數(shù)JJ河北（北京）\\L2.tif" \* MERGEFORMATINET 一條排水管的截面如圖所示，已知排水管的半徑OB＝5，水面寬AB＝8，則截面圓心O到水面的距離OC是(　　)
INCLUDEPICTURE"冊(cè)132.tif" INCLUDEPICTURE "D:\\課件\\九數(shù)JJ河北（北京）\\冊(cè)132.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數(shù)JJ河北（北京）\\冊(cè)132.tif" \* MERGEFORMATINET
A．3 　　 B．4 　　 C．3 　　 D．6
變式2[2023武漢期中]如圖是一個(gè)高速公路的隧道的橫截面，它的形狀是以O(shè)為圓心的圓的一部分，如果D是⊙O中弦AB的中點(diǎn)，CD經(jīng)過(guò)圓心O交⊙O于點(diǎn)C，AB＝24，CD＝18，則此圓的半徑OA的長(zhǎng)為_(kāi)_______．
INCLUDEPICTURE"冊(cè)133.tif" INCLUDEPICTURE "D:\\課件\\九數(shù)JJ河北（北京）\\冊(cè)133.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數(shù)JJ河北（北京）\\冊(cè)133.tif" \* MERGEFORMATINET
28.4 垂徑定理*
INCLUDEPICTURE"復(fù)習(xí)回顧.tif" INCLUDEPICTURE "復(fù)習(xí)回顧.tif" \* MERGEFORMAT INCLUDEPICTURE "D:\\課件\\九數(shù)JJ河北（北京）\\復(fù)習(xí)回顧.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數(shù)JJ河北（北京）\\復(fù)習(xí)回顧.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數(shù)JJ河北（北京）\\復(fù)習(xí)回顧.tif" \* MERGEFORMATINET
1．D　2.54°　3.
INCLUDEPICTURE"預(yù)習(xí)效果.tif" INCLUDEPICTURE "預(yù)習(xí)效果.tif" \* MERGEFORMAT INCLUDEPICTURE "D:\\課件\\九數(shù)JJ河北（北京）\\預(yù)習(xí)效果.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數(shù)JJ河北（北京）\\預(yù)習(xí)效果.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數(shù)JJ河北（北京）\\預(yù)習(xí)效果.tif" \* MERGEFORMATINET
1．平分； 平分　2.B　3.8
4．解：連接OC，
∵AB是⊙O的直徑，AB⊥CD，
∴CE＝CD＝4.
在Rt△COE中，由勾股定理，得OC＝＝＝5.∴⊙O的半徑為5.
INCLUDEPICTURE"課堂導(dǎo)學(xué).tif" INCLUDEPICTURE "課堂導(dǎo)學(xué).tif" \* MERGEFORMAT INCLUDEPICTURE "D:\\課件\\九數(shù)JJ河北（北京）\\課堂導(dǎo)學(xué).tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數(shù)JJ河北（北京）\\課堂導(dǎo)學(xué).tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數(shù)JJ河北（北京）\\課堂導(dǎo)學(xué).tif" \* MERGEFORMATINET
例1　A　變式1－1.D　變式1－2.B　
例2　A　變式2.13

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