名校
解题方法
1 . 如图,二面角
的大小为
,半径为2的球O与平面
相切于点A,与
相交于圆
,
为圆
的一条直径,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/1/2fad8040-b182-4cf6-bf2a-28c69631c26e.png?resizew=336)
(1)证明:
平面
;
(2)过球心的平面截球面所得圆称为大圆,如圆O,不过球心的平面截球面所得的圆为小圆,如圆
,过某两点的大圆上两点间的劣弧的长度叫这两点的球面距离,球面距离是球面上两点间距离的最小值.试求A、B两点间的球面距离.(如果某个
)满足
,则可将
记作
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bec3143f08cc5c757ff8fb16a2d7b9bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f785147690f83dcee0a0bc6c327e75a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047dc9795efa99b6fb9fdf9778085dab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdc11a059f6073ebacd015763cdd06ea.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/1/2fad8040-b182-4cf6-bf2a-28c69631c26e.png?resizew=336)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93cf663ee2bf1ac5c43f4306fa0cf250.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c185c12f0e23a41ad82eb4c895cbb341.png)
(2)过球心的平面截球面所得圆称为大圆,如圆O,不过球心的平面截球面所得的圆为小圆,如圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12f102439ebd1efd422f04209ecec2bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e90285b4943db2befa410d4bcec380c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4429c0a0cc9ee3e97ae68f28829635fc.png)
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