名校
解题方法
1 . 如图1,与三角形的三边都相切的圆叫做三角形的内切圆.设O是△ABC的内切圆圆心,
内是△ABC的内切圆半径,设
是△ABC的面积,
是△ABC的周长,由等面积法,可以得到
内
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/29/e3da696e-d797-4178-ab24-f0087aafa165.jpg?resizew=358)
(1)与三棱锥的四个面都相切的球叫做三棱锥的内切球.设三棱锥的体积是
,表面积是
,请用类比推理思想,写出三棱锥的内切球的半径公式
内(只写结论即可,不必写推理过程);
(2)如图2,在三棱锥
中,
,
,
两两垂直,且
,求三棱锥
的内切球半径和外接球的半径之比.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5cbff84327e964f912a54032e76ccc9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8c261982132e55c19fd25ad50c6f3b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4fcc80a88cb1dc8fd4184f5b8225814.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/29/e3da696e-d797-4178-ab24-f0087aafa165.jpg?resizew=358)
(1)与三棱锥的四个面都相切的球叫做三棱锥的内切球.设三棱锥的体积是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be54e84508decfcce6d2fcbe6c8c1a92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
(2)如图2,在三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50094bfee564d9c1b03088ac2ece28c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
您最近一年使用:0次
2021-12-29更新
|
442次组卷
|
3卷引用:四川省南充市白塔中学2022-2023学年高三上学期入学考试数学(理)试题
解题方法
2 . 开普勒说:“我珍视类比胜过任何别的东西,它是我最可信赖的老师,它能揭示自然界的秘密,”波利亚也曾说过:“类比是一个伟大的引路人,求解立体几何问题往往有赖于平面几何中的类比问题.”在选修1—2第二章《推理与证明》的学习中,我们知道,平面图形很多可以推广到空间中去,例如正三角形可以推广到正四面体,圆可以推广到球,平行四边形可以推广到平行六面体等.如图,如果四面体
中棱
,
,
两两垂直,那么称四面体
为直角四面体.请类比直角三角形
(
表示斜边上的高)中的性质给出直角四面体
中的两个性质,并给出证明.
![](https://img.xkw.com/dksih/QBM/2021/6/17/2744873475547136/2748343588134912/STEM/165b547f6ead4a82b50c3e0c4fd0adc8.png?resizew=352)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d674cc434aa1a626840c340c7dcdc96a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d004d2d115b477ade6af7ddb93db0df8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fd17a66a2af938c89e46f22e4d893b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d674cc434aa1a626840c340c7dcdc96a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3eabd5f3a86afe49dcd70571e2b96cfd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d674cc434aa1a626840c340c7dcdc96a.png)
![](https://img.xkw.com/dksih/QBM/2021/6/17/2744873475547136/2748343588134912/STEM/165b547f6ead4a82b50c3e0c4fd0adc8.png?resizew=352)
直角三角形![]() | 直角四面体![]() | |
条件 | ![]() | ![]() ![]() ![]() |
结论1 | ![]() | |
结论2 | ![]() |
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