半径为1的球面上有A，B，C三点，其中A和B的球面距离，A和C的球面距离都是π2，B和C的球面距离是π3．（1 半径为1的球面上有A、B、C三点其中A和B的球面距离与A和C...
\u534a\u5f84\u4e3a1\u7684\u7403\u9762\u4e0a\u6709A,B,C\u4e09\u70b9\uff0c\u5176\u4e2dA\u548cB\u7684\u7403\u9762\u8ddd\u79bb\uff0cA\u548cC\u7684\u7403\u9762\u8ddd\u79bb\u90fd\u662f\uff0f\u03c02\uff0cB\u548cC\u7684\u7403\u9762\u8ddd\u79bb\u662f\u03c0\uff0f3.A\u548cC\u7684\u7403\u9762\u8ddd\u79bb\u90fd\u662f\u03c0\uff0f2\uff0c 2\u03c0r\u00f7\u03c0/2=4 \u6240\u4ee5A\u4e0eC\u5bf9\u5e94\u7684\u5706\u5fc3\u89d2\u662f360\u00b0\u00f74=90\u00b0\uff0c\u540c\u6837\u7684\u9053\u7406\uff0cA\u4e0eB\u5bf9\u5e94\u7684\u5706\u5fc3\u89d2\u4e5f\u662f360\u00b0\u00f74=90\u00b0\uff0c\u4ee5\u5706\u5fc3O\u4e3a\u539f\u70b9\u5efa\u7acb\u7a7a\u95f4\u76f4\u89d2\u5750\u6807\u7cfb\uff0c\u5e76\u4ee4A=(1,0,0), B=(0,1,0),\u56e0\u4e3aB\u548cC\u7684\u7403\u9762\u8ddd\u79bb\u662f\u03c0\uff0f3. B\u4e0eC\u5bf9\u5e94\u7684\u5706\u5fc3\u89d2\u662f360\u00b0\u00f76=60\u00b0 \u6240\u4ee5C=(0,1/2\uff0c2\u5206\u4e4b\u6839\u53f73)\uff0cA\u3001B\u3001C\u7684\u5750\u6807\u90fd\u51fa\u6765\u4e86\uff0c\u95ee\u9898\u81ea\u5df1\u89e3\u51b3\u597d\u4e0d\u597d\uff01\u795d\u4f60\u8003\u8bd5\u6109\u5feb\u54c8\uff01
\u7403\u5fc3O\u4e0eA\uff0cB\uff0cC\u4e09\u70b9\u6784\u6210\u6b63\u4e09\u68f1\u9525O-ABC\uff0c\u5df2\u77e5OA=OB=OC=R=1\uff0c\u2220AOB=\u2220BOC=\u2220AOC=90\u00b0\uff0c\u7531\u6b64\u53ef\u5f97AO\u22a5\u9762BOC\uff0e\u2235S\u25b3BOC\uff1d12\u00d71\u00d71\uff1d12\uff0cS\u25b3ABC\uff1d12\u00d72\u00d7(2)2?(22)2\uff1d 32\uff0e\u8bbe\u7403\u5fc3\u5230\u9762\u7684\u8ddd\u79bb\u4e3ah\uff0c\u7531VA-BOC=VO-ABC\uff0c13\u00d7 12\u00d71\uff1d13\u00d732\u00d7h\uff0c\u5f97 h\uff1d33\uff0e\u6240\u4ee5\u7403\u5fc3O \u5230\u5e73\u9762ABC\u7684\u8ddd\u79bb 33\uff0e\u6545\u9009C\uff0e
（1）由题意知：∠AOC=| π |
| 2 |
| π |
| 2 |
| π |
| 3 |
∵OA=OB=OC=1，∴AB=AC=
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