中考數(shù)學(xué)二輪復(fù)習(xí)幾何模型重點(diǎn)突破講練專題27 切線模型（原卷版）

專題27切線模型【模型1】雙切線模型已知如圖27-1，點(diǎn)SKIPIF1<0為⊙SKIPIF1<0外一點(diǎn)，SKIPIF1<0、SKIPIF1<0是⊙SKIPIF1<0的切線，切點(diǎn)分別為SKIPIF1<0、SKIPIF1<0，根據(jù)切線的性質(zhì)，可證明SKIPIF1<0≌SKIPIF1<0,SKIPIF1<0，SKIPIF1<0垂直平分SKIPIF1<0?！灸Ｐ?】割線定理如圖27-2，已知在⊙SKIPIF1<0中，弦SKIPIF1<0、SKIPIF1<0相交于點(diǎn)SKIPIF1<0，點(diǎn)SKIPIF1<0在⊙SKIPIF1<0外SKIPIF1<0SKIPIF1<0?！咀C明】如圖27-5，連接SKIPIF1<0、SKIPIF1<0，SKIPIF1<0SKIPIF1<0，SKIPIF1<0SKIPIF1<0SKIPIF1<0∽SKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1<0【模型3】切割線定理如圖27-3，已知在⊙SKIPIF1<0中，弦SKIPIF1<0的延長(zhǎng)線交⊙SKIPIF1<0的切線SKIPIF1<0于SKIPIF1<0SKIPIF1<0SKIPIF1<0?！咀C明】如圖27-4，連接SKIPIF1<0、SKIPIF1<0，SKIPIF1<0SKIPIF1<0為⊙SKIPIF1<0的弦切角，SKIPIF1<0SKIPIF1<0又SKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1<0∽SKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1<0【例1】如圖，點(diǎn)P為⊙O外一點(diǎn)，過(guò)點(diǎn)P作⊙O的切線PA、PB，記切點(diǎn)為A、B，點(diǎn)C為⊙O上一點(diǎn)，連接AC、BC．若∠ACB＝62°，則∠APB等于（）A．68° B．64° C．58° D．56°【例2】已知：如圖，SKIPIF1<0、SKIPIF1<0是⊙SKIPIF1<0的割線，SKIPIF1<0，SKIPIF1<0，SKIPIF1<0.則SKIPIF1<0=______SKIPIF1<0.【例3】如圖，SKIPIF1<0是⊙O的直徑，射線SKIPIF1<0交⊙O于點(diǎn)SKIPIF1<0，SKIPIF1<0是劣弧SKIPIF1<0上一點(diǎn)，且SKIPIF1<0平分SKIPIF1<0，過(guò)點(diǎn)SKIPIF1<0作SKIPIF1<0于點(diǎn)SKIPIF1<0，延長(zhǎng)SKIPIF1<0和SKIPIF1<0的延長(zhǎng)線交于點(diǎn)SKIPIF1<0．(1)證明：SKIPIF1<0是⊙O的切線；(2)若SKIPIF1<0，SKIPIF1<0，求⊙O的半徑．一、單選題1．如圖，AB是⊙O的直徑，點(diǎn)M在BA的延長(zhǎng)線上，MA＝AO，MD與⊙O相切于點(diǎn)D，BC⊥AB交MD的延長(zhǎng)線于點(diǎn)C，若⊙O的半徑為2，則BC的長(zhǎng)是（）A．4 B．SKIPIF1<0 C．SKIPIF1<0 D．32．如圖，SKIPIF1<0、SKIPIF1<0分別切SKIPIF1<0于點(diǎn)SKIPIF1<0、SKIPIF1<0，點(diǎn)SKIPIF1<0為優(yōu)弧SKIPIF1<0上一點(diǎn)，若SKIPIF1<0，則SKIPIF1<0的度數(shù)為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．如圖，⊙O的半徑為SKIPIF1<0，BD是⊙O的切線，D為切點(diǎn)，過(guò)圓上一點(diǎn)C作BD的垂線，垂足為B，BC＝3，點(diǎn)A是優(yōu)弧CD的中點(diǎn)，則sin∠A的值是（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0二、填空題4．如圖，PA、PB分別與⊙O相切于A、B兩點(diǎn)，點(diǎn)C為⊙O上一點(diǎn)，連接AC、BC，若∠P＝50°，則∠ACB的度數(shù)為____________5．如圖，已知AB是SKIPIF1<0的直徑，點(diǎn)P在BA的延長(zhǎng)線上，PD與SKIPIF1<0相切于點(diǎn)D，過(guò)點(diǎn)B作PD的垂線交PD的延長(zhǎng)線于點(diǎn)C．若SKIPIF1<0的半徑為3，SKIPIF1<0，則PA的長(zhǎng)為______．6．如圖，PA，PB是SKIPIF1<0的切線，A，B為切點(diǎn)．若SKIPIF1<0，則SKIPIF1<0的大小為______．7．如圖，PA，PB是⊙O的切線，A，B是切點(diǎn)．若∠P＝45°，則∠AOB＝_____°．8．如圖，PA、PB分別切⊙O于點(diǎn)A，B，點(diǎn)E是⊙O上一點(diǎn)，且SKIPIF1<0，則SKIPIF1<0的度數(shù)為______．9．如圖，PA，PB分別切⊙O于點(diǎn)A，B，Q是優(yōu)弧SKIPIF1<0上一點(diǎn)，若∠P=40°，則∠Q的度數(shù)是________．三、解答題10．如圖，⊙O與△ABC的邊BC相切于點(diǎn)D，與AB、AC的延長(zhǎng)線分別相切于點(diǎn)E、F，連接OB，OC．(1)若∠ABC=80°，∠ACB=40°，求∠BOC的度數(shù)．(2)∠BOC與∠A有怎樣的數(shù)量關(guān)系，并說(shuō)明理由．11．如圖，已知P，PB分別與⊙O相切于點(diǎn)AB，∠APB＝60°，C為⊙O上一點(diǎn)．(1)如圖②求∠ACB的度數(shù)；(2)如圖②AE為⊙O的直徑，AB與BC相交于點(diǎn)D，若AB＝AD，求∠BAC的度數(shù)．12．如圖，CD是⊙O的切線，切點(diǎn)為D，點(diǎn)C在直徑AB的延長(zhǎng)線上．(1)求證：∠CAD＝∠BDC；(2)若tan∠BDC＝SKIPIF1<0，AC＝3，求CD的長(zhǎng)．13．如圖，在⊙O中，AB是⊙O的直徑，點(diǎn)P在BA的延長(zhǎng)線上，PD切⊙O于點(diǎn)C．SKIPIF1<0，垂足為D，連接BC．(1)求證：BC平分∠PBD；(2)若SKIPIF1<0，SKIPIF1<0，求⊙O的半徑．14．如圖，SKIPIF1<0是⊙SKIPIF1<0的直徑，SKIPIF1<0是⊙SKIPIF1<0的切線，SKIPIF1<0、SKIPIF1<0是⊙SKIPIF1<0的弦，且SKIPIF1<0，垂足為E，連接SKIPIF1<0并延長(zhǎng)，交SKIPIF1<0于點(diǎn)P．(1)求證：SKIPIF1<0；(2)若⊙SKIPIF1<0的半徑SKIPIF1<0，求線段SKIPIF1<0的長(zhǎng)．15．如圖，SKIPIF1<0為⊙SKIPIF1<0的直徑，過(guò)圓上一點(diǎn)SKIPIF1<0作⊙SKIPIF1<0的切線SKIPIF1<0交SKIPIF1<0的延長(zhǎng)線與點(diǎn)SKIPIF1<0，過(guò)點(diǎn)SKIPIF1<0作SKIPIF1<0交SKIPIF1<0于點(diǎn)SKIPIF1<0，連接SKIPIF1<0．(1)直線SKIPIF1