中考數(shù)學(xué)二輪復(fù)習(xí)重難點(diǎn)與壓軸題型專項(xiàng)突破訓(xùn)練專題09 圓的綜合問(wèn)題（重點(diǎn)突圍）(原卷版)

專題09圓的綜合問(wèn)題【中考考向?qū)Ш健磕夸汿OC\o"1-3"\h\u【直擊中考】 1【考向一利用圓性質(zhì)求角的度數(shù)】 1【考向二利用圓性質(zhì)求線段的長(zhǎng)度】 3【考向三利用圓性質(zhì)求圓的半徑】 11【考向四利用圓性質(zhì)求線段的最值】 12【考向四利用圓性質(zhì)求陰影部分的面積】 15【考向五切線的證明綜合應(yīng)用】 16【直擊中考】【考向一利用圓性質(zhì)求角的度數(shù)】例題：（2022秋·浙江杭州·九年級(jí)校聯(lián)考階段練習(xí)）如圖，四邊形SKIPIF1<0內(nèi)接于SKIPIF1<0，SKIPIF1<0，A為SKIPIF1<0中點(diǎn)，SKIPIF1<0，則SKIPIF1<0等于（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0【變式訓(xùn)練】1．（2022·湖北省直轄縣級(jí)單位·校考二模）如圖，一塊直角三角板的SKIPIF1<0角的頂點(diǎn)SKIPIF1<0落在SKIPIF1<0上，兩邊分別交SKIPIF1<0于SKIPIF1<0兩點(diǎn)，連結(jié)SKIPIF1<0，則SKIPIF1<0的度數(shù)是（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．（2022·黑龍江哈爾濱·?？级＃┤鐖D，SKIPIF1<0、SKIPIF1<0、SKIPIF1<0、SKIPIF1<0四個(gè)點(diǎn)均在SKIPIF1<0上，SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0的度數(shù)為___________．3．（2022·內(nèi)蒙古通遼·模擬預(yù)測(cè)）如圖所示，已知四邊形SKIPIF1<0是SKIPIF1<0SKIPIF1<0的一個(gè)內(nèi)接四邊形，且SKIPIF1<0，則SKIPIF1<0_______．【考向二利用圓性質(zhì)求線段的長(zhǎng)度】例題：（2022·四川綿陽(yáng)·東辰國(guó)際學(xué)校?？寄M預(yù)測(cè)）如圖，點(diǎn)A，B，C，D在SKIPIF1<0上，點(diǎn)A為SKIPIF1<0的中點(diǎn)，SKIPIF1<0交弦SKIPIF1<0于點(diǎn)E．若SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0的長(zhǎng)是（

）A．2 B．4 C．SKIPIF1<0 D．SKIPIF1<0【變式訓(xùn)練】1．（2022·江蘇鹽城·鹽城市第四中學(xué)（鹽城市藝術(shù)高級(jí)中學(xué)、鹽城市逸夫中學(xué)）?？寄M預(yù)測(cè)）如圖，以SKIPIF1<0為直徑的SKIPIF1<0與SKIPIF1<0相切于點(diǎn)SKIPIF1<0，點(diǎn)SKIPIF1<0、SKIPIF1<0在SKIPIF1<0上，連接SKIPIF1<0、SKIPIF1<0、SKIPIF1<0，連接SKIPIF1<0并延長(zhǎng)交SKIPIF1<0于點(diǎn)SKIPIF1<0，SKIPIF1<0與SKIPIF1<0交于點(diǎn)SKIPIF1<0．(1)求證：SKIPIF1<0；(2)若點(diǎn)SKIPIF1<0是弧SKIPIF1<0的中點(diǎn)，SKIPIF1<0的半徑為SKIPIF1<0，SKIPIF1<0，求SKIPIF1<0的長(zhǎng)．2．（2022·內(nèi)蒙古通遼·模擬預(yù)測(cè)）如圖，SKIPIF1<0與SKIPIF1<0的SKIPIF1<0邊相切于點(diǎn)SKIPIF1<0，與SKIPIF1<0、SKIPIF1<0邊分別交于點(diǎn)SKIPIF1<0、SKIPIF1<0，SKIPIF1<0，SKIPIF1<0是SKIPIF1<0的直徑．(1)求證：SKIPIF1<0是SKIPIF1<0的切線；(2)若SKIPIF1<0，SKIPIF1<0，求SKIPIF1<0的長(zhǎng)．3．（2022·湖北省直轄縣級(jí)單位·?？家荒＃┤鐖D，SKIPIF1<0是SKIPIF1<0的外接圓，SKIPIF1<0是SKIPIF1<0的直徑，F(xiàn)是SKIPIF1<0延長(zhǎng)線上一點(diǎn)，連接SKIPIF1<0，SKIPIF1<0，且SKIPIF1<0．(1)求證：SKIPIF1<0是SKIPIF1<0的切線；(2)若SKIPIF1<0，SKIPIF1<0，求SKIPIF1<0的長(zhǎng)．4．（2022·四川綿陽(yáng)·東辰國(guó)際學(xué)校校考模擬預(yù)測(cè)）如圖，SKIPIF1<0為SKIPIF1<0的直徑，SKIPIF1<0為弦，過(guò)點(diǎn)C的切線與SKIPIF1<0的延長(zhǎng)線交于點(diǎn)P，E為SKIPIF1<0上一點(diǎn)，且SKIPIF1<0，連接SKIPIF1<0并延長(zhǎng)交SKIPIF1<0于點(diǎn)H．(1)求證：SKIPIF1<0．(2)若SKIPIF1<0，SKIPIF1<0，求SKIPIF1<0的長(zhǎng)．【考向三利用圓性質(zhì)求圓的半徑】例題：（2022·福建福州·?？家荒＃┤鐖D，四邊形SKIPIF1<0內(nèi)接于SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0的半徑為（

）A．4 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0【變式訓(xùn)練】1．（2022·福建福州·?？家荒＃┤鐖D，SKIPIF1<0為SKIPIF1<0的直徑，P為SKIPIF1<0延長(zhǎng)線上的一點(diǎn)，過(guò)P作SKIPIF1<0的切線SKIPIF1<0，A為切點(diǎn)，SKIPIF1<0，則SKIPIF1<0的半徑等于___________．2．（2022·湖北省直轄縣級(jí)單位·校考一模）如圖，點(diǎn)A，B，C在SKIPIF1<0上，SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0的半徑為_____．3．（2022·云南文山·統(tǒng)考三模）如圖，在SKIPIF1<0中，SKIPIF1<0，D、E分別是AB、BC上的點(diǎn)，過(guò)B、D、E三點(diǎn)作SKIPIF1<0，交SKIPIF1<0延長(zhǎng)線于點(diǎn)F，SKIPIF1<0，SKIPIF1<0，SKIPIF1<0．(1)求證：SKIPIF1<0；(2)當(dāng)SKIPIF1<0與SKIPIF1<0相切于點(diǎn)D時(shí)，求SKIPIF1<0的半徑；(3)若SKIPIF1<0，求SKIPIF1<0的值．【考向四利用圓性質(zhì)求線段的最值】例題：（2022·安徽合肥·校聯(lián)考三模）如圖，SKIPIF1<0是SKIPIF1<0的直徑，SKIPIF1<0，點(diǎn)SKIPIF1<0在SKIPIF1<0上，SKIPIF1<0是SKIPIF1<0的中點(diǎn)，SKIPIF1<0是直徑SKIPIF1<0上的一動(dòng)點(diǎn)，若SKIPIF1<0，則SKIPIF1<0周長(zhǎng)的最小值為（）A．4 B．5 C．6 D．7【變式訓(xùn)練】1．（2022·廣東江門·?？家荒＃┚匦蜸KIPIF1<0中，SKIPIF1<0，SKIPIF1<0，點(diǎn)P為矩形內(nèi)一個(gè)動(dòng)點(diǎn)且滿足SKIPIF1<0，則線段SKIPIF1<0的最小值為________．2．（2022·廣東江門·校考一模）SKIPIF1<0中，SKIPIF1<0，SKIPIF1<0，點(diǎn)SKIPIF1<0為SKIPIF1<0的對(duì)稱軸上一動(dòng)點(diǎn)，過(guò)點(diǎn)SKIPIF1<0作SKIPIF1<0與SKIPIF1<0相切，SKIPIF1<0與SKIPIF1<0相交于點(diǎn)SKIPIF1<0，那么SKIPIF1<0的最大值為______________．【考向四利用圓性質(zhì)求陰影部分的面積】例題：（2022·廣東江門·?？家荒＃┤鐖D，正方形的邊長(zhǎng)為2，則圖中陰影部分的面積為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0【變式訓(xùn)練】1．（2022·湖北省直轄縣級(jí)單位·?？家荒＃┤鐖D，在半徑為2，圓心角為SKIPIF1<0的扇形內(nèi)，以SKIPIF1<0為直徑作半圓，交弦SKIPIF1<0于點(diǎn)D，則圖中陰影部分的面積是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．（2022春·九年級(jí)課時(shí)練習(xí)）如圖，矩形SKIPIF1<0中，SKIPIF1<0，SKIPIF1<0，SKIPIF1<0是SKIPIF1<0中點(diǎn)，以點(diǎn)SKIPIF1<0為圓心，SKIPIF1<0為半徑作弧交SKIPIF1<0于點(diǎn)SKIPIF1<0，以點(diǎn)SKIPIF1<0為圓心，SKIPIF1<0為半徑作弧交SKIPIF1<0于點(diǎn)SKIPIF1<0，則圖中陰影部分面積的差SKIPIF1<0為______．3．（2022秋·四川瀘州·九年級(jí)統(tǒng)考期中）如圖，SKIPIF1<0，SKIPIF1<0分別是SKIPIF1<0的直徑和弦，半徑SKIPIF1<0于點(diǎn)SKIPIF1<0．過(guò)點(diǎn)SKIPIF1<0作SKIPIF1<0的切線與SKIPIF1<0的延長(zhǎng)線交于點(diǎn)SKIPIF1<0，SKIPIF1<0，SKIPIF1<0的延長(zhǎng)線交于點(diǎn)SKIPIF1<0．(1)求證：SKIPIF1<0是SKIPIF1<0的切線；(2)若SKIPIF1<0，SKIPIF1<0，求圖中陰影部分的面積．4．（2022·江蘇揚(yáng)州·?？既＃┤鐖D，Rt△ABC中，SKIPIF1<0，SKIPIF1<0，SKIPIF1<0為SKIPIF1<0上一點(diǎn)，SKIPIF1<0，以SKIPIF1<0為圓心，以SKIPIF1<0為半徑作圓與SKIPIF1<0相交于點(diǎn)SKIPIF1<0，點(diǎn)SKIPIF1<0是⊙O與線段BC的公共點(diǎn)，連接SKIPIF1<0，并且SKIPIF1<0．(1)求證：SKIPIF1<0是⊙O的切線；(2)求圖中陰影部分的面積．5．（2022秋·全國(guó)·九年級(jí)專題練習(xí)）如圖，已知SKIPIF1<0，SKIPIF1<0為SKIPIF1<0的直徑，過(guò)點(diǎn)A作弦SKIPIF1<0垂直于直徑SKIPIF1<0于F，點(diǎn)B恰好為SKIPIF1<0的中點(diǎn)，連接SKIPIF1<0，SKIPIF1<0．(1)求證：SKIPIF1<0；(2)若SKIPIF1<0，求SKIPIF1<0的半徑；(3)在（2）的條件下，求陰影部分的面積．【考向五切線的證明綜合應(yīng)用】例題：（2022·湖南株洲·?？级＃┤鐖D，在菱形SKIPIF1<0中，SKIPIF1<0是對(duì)角線SKIPIF1<0上一點(diǎn)SKIPIF1<0，SKIPIF1<0，垂足為SKIPIF1<0，以SKIPIF1<0為半徑的SKIPIF1<0分別交SKIPIF1<0于點(diǎn)SKIPIF1<0，交SKIPIF1<0的延長(zhǎng)線于點(diǎn)SKIPIF1<0，SKIPIF1<0與SKIPIF1<0交于點(diǎn)SKIPIF1<0．(1)求證：SKIPIF1<0是SKIPIF1<0的切線；(2)若SKIPIF1<0是SKIPIF1<0的中點(diǎn)，SKIP