名校
解题方法
1 . 已知正四面体
棱长为2,点
分别是
,
,
内切圆上的动点,现有下列四个命题:
①对于任意点
,都存在点
,使
;
②存在
,使直线
平面
;
③当
最小时,三棱锥
的体积为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0467b0675c3ecfb282cc88255284d3e1.png)
④当
最大时,顶点
到平面
的距离的最大值为
.
其中正确的有___________ .(填选正确的序号即可)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f7807638578edd712265463a7a5eab0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab2a2834d80ff574e79eae8ca8d4e94f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ac451db3443cabb204f96c31fd4a02e.png)
①对于任意点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9cb8e6ff801523b0304576cd69fd2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/797e67927616b141ed7c6b83f8b6f4fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c89d54457ad06f095a8643cf3c77923.png)
②存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5425108c557f0f21474c045334f97d9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85e39cbda9b51329928487a7462cb550.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
③当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6b9ffc9d4fbb08792f487b787c71c8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d919276bf6174bdf850673cd38284cda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0467b0675c3ecfb282cc88255284d3e1.png)
④当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6b9ffc9d4fbb08792f487b787c71c8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56448a74c1b8430c425d79d626764f4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/839c7616cd0d90265f4b2c9c021254fe.png)
其中正确的有
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2024-06-05更新
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363次组卷
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2卷引用:辽宁省部分高中2023-2024学年高三下学期第三次模拟考试数学试题