1 . 已知直线
与圆
相交于
两点,下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3683fd5cbf7b7bdef462a3d38ce4eff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9be2c91c4ace79b6d3ce4e86681f2b58.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
A.若圆![]() ![]() ![]() |
B.![]() ![]() |
C.当![]() ![]() ![]() ![]() ![]() |
D.若![]() ![]() ![]() |
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2 . 若直线
与
交于
,
两点,则
面积的最大值为_________ ,写出满足“
面积最大”的
的一个值________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/816d1f63b737faba12ab856d7e5dc885.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8159f28f6c287fb3479678d6e1424217.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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3 . 直线
,被圆
截得最短弦的长为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/366a3fa39aa395b1405fbc866a516b8b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51583192ffb8fae8189fe500e972ba6d.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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4 . 已知圆
的圆心与抛物线
的焦点关于直线
对称,直线
与
相交于
两点,且
,则圆
的标准方程为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e42102c1c07562853219ca5918803a27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d77f5191798242b7b9b88a75e17e4425.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/089243ad31b799d65b9e86ec2a116188.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0907a673d52825cd7df84b400972d4b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
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5 . 已知直线
与圆
交于
两点,则
的最小值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fad8d7d3275c4d36b991727e3578a43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c424f7c2786a4c14d9efe94a065cefe3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4dfec890cdfdda355e19463f3be813.png)
A.2 | B.3 | C.4 | D.6 |
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|
395次组卷
|
3卷引用:2024年高考全国甲卷数学(文)真题
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6 . 已知直线
与圆
交于
,
两点,
为坐标原点,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e3d627f5fbd04271389d503942d233.png)
______ ,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d8e20f99a4c67a3dd6f0787d64b3ba5.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fceb9eb57ca36db386ffafeda213599c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/545b79010f9992c67601e7655eda416c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e3d627f5fbd04271389d503942d233.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d8e20f99a4c67a3dd6f0787d64b3ba5.png)
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7 . 已知b是
的等差中项,直线
与圆
交于
两点,则
的最小值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20cda097a4e7c41100e573d8304ee066.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50f6e1f67dc15c3cf135a78af95c70fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c99fd44ea14ac1cf7707062a5a6debd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2401bc9c26cc3b0b8384c7139bd58fff.png)
A.1 | B.2 | C.4 | D.![]() |
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|
2934次组卷
|
5卷引用:2024年高考全国甲卷数学(理)真题
名校
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8 . 平面几何中有定理:若点
为锐角
的外心,直线
,
,
分别与锐角
外接圆交于另外一点
,
,
,则
,若锐角
的外接圆方程为
,且该圆与
轴的交点分别为
,
,则六边形
的面积的最大值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cdba1337ec85fa9722cb4b320a82ae6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63a253c7fdf589ee3dece13d5b5b5732.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7c314398e26ffc7164b82946eeb4273.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3953cec61ac602ce5eb59b7912352179.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4c8a9c4957431681ddfc77895a88508.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfdceec9c7010b2ad114e0d72f33d97f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/225b8653f0db0218af993e5de6531dde.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b423e24a65f50b9ca1caa09c3fafdb51.png)
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9 . 相交弦定理是平面几何中关于圆的一个重要定理:圆内的两条相交弦,被交点分成的两条线段长的积相等,已知圆
的半径为
,弦
,
相交于点
.且
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d9934cf2feb65b00392ba39d8242e47.png)
A.![]() |
B.![]() |
C.当![]() ![]() ![]() |
D.当![]() ![]() ![]() |
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10 . 已知直线
与圆C:
相交于A,B两点,且
,则实数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c57bbef89a37f1a3808c0ceeac0c22.png)
____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe567b482938a45840cf770053fd64fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/284b0d767c5e2be6b01cbd33fe5eb931.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57dfc9d1109fe41145cc892b5702d9fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c57bbef89a37f1a3808c0ceeac0c22.png)
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