新高考數(shù)學(xué)二輪復(fù)習(xí)講義專題19 直線和圓（原卷版）

專題19直線和圓【考點(diǎn)專題】1．直線方程的五種形式名稱方程適用范圍點(diǎn)斜式y(tǒng)－y0＝k(x－x0)不含直線x＝x0斜截式y(tǒng)＝kx＋b不含垂直于x軸的直線兩點(diǎn)式eq\f(y－y1,y2－y1)＝eq\f(x－x1,x2－x1)(x1≠x2，y1≠y2)不含直線x＝x1和直線y＝y(tǒng)1截距式eq\f(x,a)＋eq\f(y,b)＝1不含垂直于坐標(biāo)軸和過原點(diǎn)的直線一般式Ax＋By＋C＝0(A2＋B2≠0)平面直角坐標(biāo)系內(nèi)的直線都適用2．兩條直線的位置關(guān)系(1)兩條直線平行與垂直①兩條直線平行：(ⅰ)對(duì)于兩條不重合的直線l1，l2，若其斜率分別為k1，k2，則有l(wèi)1∥l2?k1＝k2.(ⅱ)當(dāng)直線l1，l2不重合且斜率都不存在時(shí)，l1∥l2.②兩條直線垂直：(ⅰ)如果兩條直線l1，l2的斜率存在，設(shè)為k1，k2，則有l(wèi)1⊥l2?k1·k2＝－1.(ⅱ)當(dāng)其中一條直線的斜率不存在，而另一條的斜率為0時(shí)，l1⊥l2.(2)兩條直線的交點(diǎn)直線l1：A1x＋B1y＋C1＝0，l2：A2x＋B2y＋C2＝0，則l1與l2的交點(diǎn)坐標(biāo)就是方程組eq\b\lc\{\rc\(\a\vs4\al\co1(A1x＋B1y＋C1＝0，,A2x＋B2y＋C2＝0))的解．3．幾種距離(1)兩點(diǎn)P1(x1，y1)，P2(x2，y2)之間的距離|P1P2|＝eq\r(x2－x12＋y2－y12).(2)點(diǎn)P0(x0，y0)到直線l：Ax＋By＋C＝0的距離d＝eq\f(|Ax0＋By0＋C|,\r(A2＋B2)).(3)兩條平行線Ax＋By＋C1＝0與Ax＋By＋C2＝0(其中C1≠C2)間的距離d＝eq\f(|C1－C2|,\r(A2＋B2)).4圓的定義與方程定義平面內(nèi)到定點(diǎn)的距離等于定長(zhǎng)的點(diǎn)的軌跡叫做圓方程標(biāo)準(zhǔn)式(x－a)2＋(y－b)2＝r2(r>0)圓心為(a，b)半徑為r一般式x2＋y2＋Dx＋Ey＋F＝0充要條件：D2＋E2－4F>0圓心坐標(biāo)：eq\b\lc\(\rc\)(\a\vs4\al\co1(－\f(D,2)，－\f(E,2)))半徑r＝eq\f(1,2)eq\r(D2＋E2－4F)5．判斷直線與圓的位置關(guān)系常用的兩種方法(1)幾何法：利用圓心到直線的距離d和圓的半徑r的大小關(guān)系．(最重要)d<r?相交；d＝r?相切；d>r?相離．(2)代數(shù)法：eq\o(→,\s\up7(判別式),\s\do5(Δ＝b2－4ac))eq\b\lc\{\rc\(\a\vs4\al\co1(>0?相交,＝0?相切,<0?相離))6．圓與圓的位置關(guān)系設(shè)圓O1：(x－a1)2＋(y－b1)2＝req\o\al(2,1)(r1>0)，O2：(x－a2)2＋(y－b2)2＝req\o\al(2,2)(r2>0)方法位置關(guān)系幾何法：圓心距d與r1，r2的關(guān)系代數(shù)法：聯(lián)立兩圓方程組成方程組的解的情況外離d>r1＋r2無解外切d＝r1＋r2一組實(shí)數(shù)解相交|r1－r2|<d<r1＋r2兩組不同的實(shí)數(shù)解內(nèi)切d＝|r1－r2|(r1≠r2)一組實(shí)數(shù)解內(nèi)含0≤d<|r1－r2|(r1≠r2)無解【方法技巧】處理定點(diǎn)問題的思路：（1）確定題目中的核心變量（此處設(shè)為SKIPIF1<0），（2）利用條件找到SKIPIF1<0與過定點(diǎn)的曲線SKIPIF1<0的聯(lián)系，得到有關(guān)SKIPIF1<0與SKIPIF1<0的等式，（3）所謂定點(diǎn)，是指存在一個(gè)特殊的點(diǎn)SKIPIF1<0，使得無論SKIPIF1<0的值如何變化，等式恒成立，此時(shí)要將關(guān)于SKIPIF1<0與SKIPIF1<0的等式進(jìn)行變形，直至找到SKIPIF1<0，①若等式的形式為整式，則考慮將含SKIPIF1<0的式子歸為一組，變形為“SKIPIF1<0”的形式，讓括號(hào)中式子等于0，求出定點(diǎn)；②若等式的形式是分式，一方面可考慮讓分子等于0，一方面考慮分子和分母為倍數(shù)關(guān)系，可消去SKIPIF1<0變?yōu)槌?shù).【核心題型】題型一：待定系數(shù)法求直線方程1．（2022·北京·統(tǒng)考模擬預(yù)測(cè)）已知圓SKIPIF1<0，直線l過點(diǎn)SKIPIF1<0且傾斜角為SKIPIF1<0，則“直線l與圓C相切”是“SKIPIF1<0”的（

）A．充分不必要條件 B．必要不充分條件C．充要條件 D．既不充分也不必要條件2．（2023秋·北京石景山·高三統(tǒng)考期末）已知直線SKIPIF1<0與圓SKIPIF1<0交于A，B兩點(diǎn)，則線段SKIPIF1<0的垂直平分線方程為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．（2022·廣東中山·中山紀(jì)念中學(xué)?？寄M預(yù)測(cè)）已知直線l經(jīng)過點(diǎn)SKIPIF1<0，且被圓SKIPIF1<0截得的弦長(zhǎng)為4，則直線l的方程是

（

）A．SKIPIF1<0 B．SKIPIF1<0或SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0或SKIPIF1<0題型二：已知兩直線位置求參數(shù)或者范圍4．（2023·吉林·東北師大附中?？级＃┲本€SKIPIF1<0的方程為SKIPIF1<0，當(dāng)原點(diǎn)SKIPIF1<0到直線SKIPIF1<0的距離最大時(shí)，SKIPIF1<0的值為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<05．（2023秋·浙江嘉興·高三統(tǒng)考期末）已知圓SKIPIF1<0過點(diǎn)SKIPIF1<0，且圓心在SKIPIF1<0軸的正半軸上，直線SKIPIF1<0被圓SKIPIF1<0所截得的弦長(zhǎng)為SKIPIF1<0，則過圓心SKIPIF1<0且與直線SKIPIF1<0垂直的直線的方程為（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<06．（2023·吉林·統(tǒng)考二模）已知SKIPIF1<0，若直線SKIPIF1<0與直線SKIPIF1<0垂直，則SKIPIF1<0的最小值為（

）A．1 B．3 C．8 D．9題型三：直線的定點(diǎn)問題7．（2023·浙江嘉興·統(tǒng)考模擬預(yù)測(cè)）已知點(diǎn)SKIPIF1<0，SKIPIF1<0與直線SKIPIF1<0，若在直線SKIPIF1<0上存在點(diǎn)SKIPIF1<0，使得SKIPIF1<0，則實(shí)數(shù)SKIPIF1<0的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<08．（2023·貴州畢節(jié)·統(tǒng)考一模）已知點(diǎn)SKIPIF1<0在直線SKIPIF1<0上，過點(diǎn)SKIPIF1<0作圓SKIPIF1<0的兩條切線，切點(diǎn)分別為SKIPIF1<0，則圓心SKIPIF1<0到直線SKIPIF1<0的距離的最大值為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．1 D．SKIPIF1<0題型四：直線有關(guān)的對(duì)稱問題9．（2023秋·貴州貴陽(yáng)·高三統(tǒng)考期末）若SKIPIF1<0為圓SKIPIF1<0上的動(dòng)點(diǎn)，當(dāng)SKIPIF1<0到直線SKIPIF1<0的距離取得最大值時(shí)，直線SKIPIF1<0的斜率為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<010．（2023·北京平谷·統(tǒng)考模擬預(yù)測(cè)）點(diǎn)M、N在圓SKIPIF1<0上，且M、N兩點(diǎn)關(guān)于直線SKIPIF1<0對(duì)稱，則圓C的半徑（

）A．最大值為SKIPIF1<0 B．最小值為SKIPIF1<0 C．最小值為SKIPIF1<0 D．最大值為SKIPIF1<011．（2023·陜西西安·?？寄M預(yù)測(cè)）SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，一束光線從點(diǎn)SKIPIF1<0出發(fā)射到SKIPIF1<0上的點(diǎn)SKIPIF1<0，經(jīng)SKIPIF1<0反射后，再經(jīng)SKIPIF1<0反射，落到線段SKIPIF1<0上（不含端點(diǎn)），則SKIPIF1<0的斜率的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<012．（2023秋·江西吉安·高三統(tǒng)考期末）已知點(diǎn)SKIPIF1<0，SKIPIF1<0，若直線SKIPIF1<0關(guān)于SKIPIF1<0的對(duì)稱直線SKIPIF1<0與圓SKIPIF1<0：SKIPIF1<0交于SKIPIF1<0，SKIPIF1<0兩點(diǎn)，則SKIPIF1<0的最小值為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0題型五：幾何法求圓的方程13．（2022秋·河南·高三信陽(yáng)高中校聯(lián)考期末）已知點(diǎn)SKIPIF1<0是圓SKIPIF1<0上的任意一點(diǎn)，點(diǎn)SKIPIF1<0，SKIPIF1<0分別為圓SKIPIF1<0上的兩個(gè)不同的動(dòng)點(diǎn)，且SKIPIF1<0，點(diǎn)SKIPIF1<0為線段SKIPIF1<0的中點(diǎn)，則SKIPIF1<0的最小值為（

）A．11 B．12 C．13 D．1414．（2023·全國(guó)·高三專題練習(xí)）已知SKIPIF1<0是圓SKIPIF1<0上兩點(diǎn)，且SKIPIF1<0．若存在SKIPIF1<0，使得直線SKIPIF1<0與SKIPIF1<0的交點(diǎn)SKIPIF1<0恰為SKIPIF1<0的中點(diǎn)，則實(shí)數(shù)SKIPIF1<0的取值范圍為（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<015．（2022·全國(guó)·高三專題練習(xí)）在平面直角坐標(biāo)系中，動(dòng)圓SKIPIF1<0與直線SKIPIF1<0相切，則面積最大的圓的標(biāo)準(zhǔn)方程為（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0題型六：待定系數(shù)法求圓的方程16．（2023·山西·校聯(lián)考模擬預(yù)測(cè)）已知圓SKIPIF1<0：SKIPIF1<0的圓心到直線SKIPIF1<0的距離為SKIPIF1<0，則圓SKIPIF1<0與圓SKIPIF1<0：SKIPIF1<0的公切線共有（

）A．0條 B．1條 C．2條 D．3條17．（2023·全國(guó)·高三專題練習(xí)）與直線SKIPIF1<0和圓SKIPIF1<0都相切的半徑最小的圓的方程是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<018．（2023·全國(guó)·高三專題練習(xí)）如圖，點(diǎn)A，B，D在圓Γ上，點(diǎn)C在圓Γ內(nèi)，SKIPIF1<0，若SKIPIF1<0，且SKIPIF1<0與SKIPIF1<0共線，則圓Γ的周長(zhǎng)為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0題型七：幾何法求弦長(zhǎng)19．（2023·全國(guó)·模擬預(yù)測(cè)）若直線SKIPIF1<0與直線SKIPIF1<0被圓SKIPIF1<0截得的弦長(zhǎng)之比為SKIPIF1<0，則圓C的面積為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<020．（2023秋·河南·高三校聯(lián)考期末）在平面直角坐標(biāo)系SKIPIF1<0中，已知圓SKIPIF1<0SKIPIF1<0SKIPIF1<0被SKIPIF1<0軸截得的弦長(zhǎng)為2，且與直線SKIPIF1<0相切，則實(shí)數(shù)SKIPIF1<0的值為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．3 D．SKIPIF1<021．（2022秋·四川廣安·高三四川省鄰水縣第二中學(xué)?？茧A段練習(xí)）已知雙曲線SKIPIF1<0的漸近線被圓SKIPIF1<0截得的弦長(zhǎng)為SKIPIF1<0，則正實(shí)數(shù)SKIPIF1<0的值為（

）A．8 B．4 C．1 D．SKIPIF1<0題型八：圓或者直線上的點(diǎn)的距離問題22．（2023·福建福州·統(tǒng)考二模）已知SKIPIF1<0，SKIPIF1<0關(guān)于直線SKIPIF1<0對(duì)稱的圓記為SKIPIF1<0，點(diǎn)E，F(xiàn)分別為SKIPIF1<0，SKIPIF1<0上的動(dòng)點(diǎn)，EF長(zhǎng)度的最小值為4，則SKIPIF1<0（

）A．SKIPIF1<0或SKIPIF1<0 B．SKIPIF1<0或SKIPIF1<0 C．SKIPIF1<0或SKIPIF1<0 D．SKIPIF1<0或SKIPIF1<023．（2023·陜西寶雞·校聯(lián)考模擬預(yù)測(cè)）在直角坐標(biāo)系xOy中，已知點(diǎn)P是圓O：SKIPIF1<0上一動(dòng)點(diǎn)，若直線l：SKIPIF1<0上存在點(diǎn)Q，滿足線段PQ的中點(diǎn)也始終在圓O上，則k的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<024．（2022秋·江西萍鄉(xiāng)·高三統(tǒng)考期末）點(diǎn)SKIPIF1<0為拋物線SKIPIF1<0上任意一點(diǎn)，點(diǎn)SKIPIF1<0為圓SKIPIF1<0上任意一點(diǎn)，SKIPIF1<0為直線SKIPIF1<0的定點(diǎn)，則SKIPIF1<0的最小值為（

）A．2 B．SKIPIF1<0 C．3 D．SKIPIF1<0題型九：直線和圓的綜合問題25．（2023·重慶·統(tǒng)考二模）過拋物線SKIPIF1<0的焦點(diǎn)SKIPIF1<0作斜率分別為SKIPIF1<0的兩條不同的直線SKIPIF1<0，且SKIPIF1<0相交于點(diǎn)SKIPIF1<0，SKIPIF1<0，SKIPIF1<0相交于點(diǎn)SKIPIF1<0，SKIPIF1<0．以SKIPIF1<0，SKIPIF1<0為直徑的圓SKIPIF1<0，圓SKIPIF1<0為圓心SKIPIF1<0的公共弦所在的直線記為SKIPIF1<0．(1)若SKIPIF1<0，求SKIPIF1<0；(2)若SKIPIF1<0，求點(diǎn)SKIPIF1<0到直線SKIPIF1<0的距離的最小值．26．（2023·湖北武漢·統(tǒng)考模擬預(yù)測(cè)）過坐標(biāo)原點(diǎn)SKIPIF1<0作圓SKIPIF1<0的兩條切線，設(shè)切點(diǎn)為SKIPIF1<0，直線SKIPIF1<0恰為拋物SKIPIF1<0的準(zhǔn)線.(1)求拋物線SKIPIF1<0的標(biāo)準(zhǔn)方程；(2)設(shè)點(diǎn)SKIPIF1<0是圓SKIPIF1<0上的動(dòng)點(diǎn)，拋物線SKIPIF1<0上四點(diǎn)SKIPIF1<0滿足：SKIPIF1<0，設(shè)SKIPIF1<0中點(diǎn)為SKIPIF1<0.（i）求直線SKIPIF1<0的斜率；（ii）設(shè)SKIPIF1<0面積為SKIPIF1<0，求SKIPIF1<0的最大值.27．（2023·全國(guó)·高三專題練習(xí)）已知橢圓C：SKIPIF1<0上點(diǎn)SKIPIF1<0與圓SKIPIF1<0上點(diǎn)M的距離的最大值為SKIPIF1<0.(1)求橢圓C的方程；(2)動(dòng)直線l與橢圓C交于A，B兩點(diǎn)，且以AB為直徑的圓過點(diǎn)SKIPIF1<0（Q與A，B不重合），證明：動(dòng)直線l過定點(diǎn)，并求出該定點(diǎn)坐標(biāo).【高考必刷】一、單選題28．（2023·重慶·統(tǒng)考二模）已知點(diǎn)SKIPIF1<0，圓SKIPIF1<0，若在圓SKIPIF1<0上存在唯一的點(diǎn)SKIPIF1<0使得SKIPIF1<0，則SKIPIF1<0可以為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<029．（2023·黑龍江哈爾濱·哈爾濱三中?？家荒＃┮阎猄KIPIF1<0，SKIPIF1<0，若直線SKIPIF1<0上存在點(diǎn)SKIPIF1<0，使得SKIPIF1<0，則實(shí)數(shù)SKIPIF1<0的取值范圍為（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<030．（2023·陜西安康·統(tǒng)考二模）已知直線SKIPIF1<0：SKIPIF1<0，SKIPIF1<0：SKIPIF1<0，則“SKIPIF1<0”是“SKIPIF1<0”的（

）A．充分不必要條件 B．必要不充分條件C．充要條件 D．既不充分也不必要條件31．（2023·貴州貴陽(yáng)·統(tǒng)考一模）已知直線SKIPIF1<0，直線SKIPIF1<0，其中實(shí)數(shù)SKIPIF1<0，則直線SKIPIF1<0與SKIPIF1<0的交點(diǎn)位于第一象限的概率為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<032．（2023·山東·煙臺(tái)二中校考模擬預(yù)測(cè)）已知雙曲線SKIPIF1<0的離心率為3，斜率為SKIPIF1<0的直線SKIPIF1<0分別交F的左右兩支于A，B兩點(diǎn)，直線SKIPIF1<0分別交F的左、右兩支于C，D兩點(diǎn)，SKIPIF1<0，SKIPIF1<0交SKIPIF1<0于點(diǎn)E，點(diǎn)E恒在直線l上，若直線l的斜率存在，則直線的方程為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<033．（2023·河北邢臺(tái)·校聯(lián)考模擬預(yù)測(cè)）已知點(diǎn)SKIPIF1<0，圓SKIPIF1<0，過點(diǎn)SKIPIF1<0的直線SKIPIF1<0與圓SKIPIF1<0交于SKIPIF1<0，SKIPIF1<0兩點(diǎn)，則SKIPIF1<0的最大值為（

）A．SKIPIF1<0 B．12 C．SKIPIF1<0 D．SKIPIF1<034．（2023·全國(guó)·本溪高中校聯(lián)考模擬預(yù)測(cè)）已知O為平面點(diǎn)角坐標(biāo)系的原點(diǎn)，點(diǎn)SKIPIF1<0，B為圓SKIPIF1<0上動(dòng)點(diǎn)，記經(jīng)過A、B的直線為l，以O(shè)為圓心與l相切的圓的面積為SKIPIF1<0，經(jīng)過O、A、B三點(diǎn)的圓的面積為SKIPIF1<0，則SKIPIF1<0的最大值為（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0二、多選題35．（2023·湖南·模擬預(yù)測(cè)）已知圓SKIPIF1<0：SKIPIF1<0與圓SKIPIF1<0：SKIPIF1<0，則下列說法正確的是（

）A．若圓SKIPIF1<0與x軸相切，則SKIPIF1<0B．直線SKIPIF1<0與圓SKIPIF1<0始終有兩個(gè)交點(diǎn)C．若SKIPIF1<0，則圓SKIPIF1<0與圓SKIPIF1<0相離D．若圓SKIPIF1<0與圓SKIPIF1<0存在公共弦，則公共弦所在的直線方程為SKIPIF1<036．（2023·湖北·統(tǒng)考模擬預(yù)測(cè)）已知直線SKIPIF1<0交SKIPIF1<0軸于點(diǎn)P，圓SKIPIF1<0，過點(diǎn)P作圓M的兩條切線，切點(diǎn)分別為A，B，直線SKIPIF1<0與SKIPIF1<0交于點(diǎn)C，則（

）A．若直線l與圓M相切，則SKIPIF1<0B．當(dāng)SKIPIF1<0時(shí)，四邊形SKIPIF1<0的面積為SKIPIF1<0C．直線SKIPIF1<0經(jīng)過一定點(diǎn)D．已知點(diǎn)SKIPIF1<0，則SKIPIF1<0為定值37．（2023·山西·校聯(lián)考模擬預(yù)測(cè)）已知圓SKIPIF1<0，點(diǎn)SKIPIF1<0為直線SKIPIF1<0上的動(dòng)點(diǎn)，則下列說法正確的是（

）A．圓心SKIPIF1<0到直線SKIPIF1<0的最大距離為8B．若直線SKIPIF1<0平分圓SKIPIF1<0的周長(zhǎng)，則SKIPIF1<0C．若圓SKIPIF1<0上至少有三個(gè)點(diǎn)到直線SKIPIF1<0的距離為SKIPIF1<0，則SKIPIF1<0D．若SKIPIF1<0，過點(diǎn)SKIPIF1<0作圓SKIPIF1<0的兩條切線，切點(diǎn)為SKIPIF1<0，SKIPIF1<0，當(dāng)點(diǎn)SKIPIF1<0坐標(biāo)為SKIPIF1<0時(shí)，SKIPIF1<0有最大值38．（2023·湖南·湖南師大附中校聯(lián)考模擬預(yù)測(cè)）已知SKIPIF1<0為圓SKIPIF1<0上的兩點(diǎn)，SKIPIF1<0為直線SKIPIF1<0上一動(dòng)點(diǎn)，則（

）A．直線SKIPIF1<0與圓SKIPIF1<0相離B．當(dāng)SKIPIF1<0為兩定點(diǎn)時(shí)，滿足SKIPIF1<0的點(diǎn)SKIPIF1<0有2個(gè)C．當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0的最大值是SKIPIF1<0D．當(dāng)SKIPIF1<0為圓SKIPIF1<0的兩條切線時(shí)，直線SKIPIF1<0過定點(diǎn)SKIPIF1<0三、填空題39．（2023·云南曲靖·曲靖一中?？寄M預(yù)測(cè)）已知橢圓SKIPIF1<0，圓SKIP