奥数之家
奥数论坛
简短留言
| 首页 | 竞赛大纲 | 优秀前辈 | 视频提示 | 专题讲座 | 论文锦集 | 综合训练 | 修身养性 | 家教平台 | 奥数论坛 |
 
The 38th British Mathematical Olympiad
2002年第38届英国奥林匹克数学竞赛
  1. From the foot of an altitude in an acute-angled triangle perpendiculars are drawn to the other two sides. Show that the distance between their feet is independent of the choice of altitude .
  2. n people wish to sit at a round table which has n chairs. The first person takes an seat. The second person sits one place to the right of the first person, the third person sits two places to the right of the second person, the fourth person sits three places to the right of the third person and so on. For which n is this possible ?
  3. The real sequence x1, x1, x2, ... is defined by x0 = 1, xn+1 = (3xn + √(5xn2 - 4) )/2. Show that all the terms are integers .
  4. S1, S2, ... , Sn are spheres of radius 1 arranged so that each touches exactly two others. P is a point outside all the spheres. Let x1, x2, ... , xn be the distances from P to the n points of contact between two spheres and y1, y2, ... , yn be the lengths of the tangents from P to the spheres. Show that x1x2 ... xn ≥ y1y2 ... yn .
点击此处查看相关视频讲解
在方框内输入单词或词组
建议使用:IE 6.0及以上版本浏览器。不支持 Netscape浏览器。 本站空间由北京师范大学提供
Copyright © 2005-2007 aoshoo.com All Rights Reserved 滇ICP备05000048号
MSN:shuxvecheng@hotmail.com QQ:316180036 E-mail:aoshoo@sina.com 电话:15810289082