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【最新试卷】三角形外心性质,向量与三角综合巧算!

  • 2026-04-03 00:22:52
【最新试卷】三角形外心性质,向量与三角综合巧算!
unsetunset📝25~26高三下·2026·山东滨州一模·第14题unsetunset

已知点为所在平面内一点，，，若，则的取值范围为_______.

(往下翻查看答案和解析)

unsetunset✅ 答案unsetunset
unsetunset🔍 解析unsetunset

由，所以点为的外心.

因为，所以.

设，再以点为原点，分别以、所在直线为、轴建立平面直角坐标系，如图：

则，，，，

所以.

又因为，所以，即.

又因为，所以点在优弧上，所以落在角的终边上.

由三角函数的定义有，，即，.

所以，

又因为，所以，

，， 所以.

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  1. CONNECT:[ UseTime:0.000398s ] mysql:host=127.0.0.1;port=3306;dbname=www_sjds;charset=utf8mb4
  2. SHOW FULL COLUMNS FROM `fenlei` [ RunTime:0.000588s ]
  3. SELECT * FROM `fenlei` WHERE `fid` = 0 [ RunTime:0.002102s ]
  4. SELECT * FROM `fenlei` WHERE `fid` = 63 [ RunTime:0.001771s ]
  5. SHOW FULL COLUMNS FROM `set` [ RunTime:0.000601s ]
  6. SELECT * FROM `set` [ RunTime:0.000246s ]
  7. SHOW FULL COLUMNS FROM `article` [ RunTime:0.000538s ]
  8. SELECT * FROM `article` WHERE `id` = 471052 LIMIT 1 [ RunTime:0.000446s ]
  9. UPDATE `article` SET `lasttime` = 1775419246 WHERE `id` = 471052 [ RunTime:0.001583s ]
  10. SELECT * FROM `fenlei` WHERE `id` = 65 LIMIT 1 [ RunTime:0.000255s ]
  11. SELECT * FROM `article` WHERE `id` < 471052 ORDER BY `id` DESC LIMIT 1 [ RunTime:0.000410s ]
  12. SELECT * FROM `article` WHERE `id` > 471052 ORDER BY `id` ASC LIMIT 1 [ RunTime:0.006082s ]
  13. SELECT * FROM `article` WHERE `id` < 471052 ORDER BY `id` DESC LIMIT 10 [ RunTime:0.003645s ]
  14. SELECT * FROM `article` WHERE `id` < 471052 ORDER BY `id` DESC LIMIT 10,10 [ RunTime:0.000724s ]
  15. SELECT * FROM `article` WHERE `id` < 471052 ORDER BY `id` DESC LIMIT 20,10 [ RunTime:0.003873s ]
0.104087s