We'll prove angle AFD = angle BDE = angle CEF. If two of the angles are the same, it's easy to prove all three are equal. WLOG, suppose angle AFD < angle BDE < angle CEF. Consider the distance from D to AC, d(D, AC) and the distance from E to AB, d(E, AB), we have d(D, AC) < d(E, AB), therefore angle A < angle B. Similarly, angle B < angle C. Now we have angle ADF > angle BED > angle CFE (sum of angles of a triangle is 180 degrees). But angle ADF + angle BDE = 120 degrees = angle AFD + angle CFE, which is a contradiction. |
can be proved in the same way. |
What if there is an obtuse angle in A, B, C? Maybe you need to discuss a few cases. When this problem appeared in WXC on March 1, two correct solutions were obtained that day (one by fzy, one by mathfun). The person who posted the problem said that his friend had already found a simple solution, and later he revealed that the method was almost the same as fzy's (I personally think this is the simplest; mathfun's is simple too compared to IBM's). A few days later, another guy, coro, came up with another proof. It is a little more complicated and only handles one case, but I think it is correct for that case. IBM's method discusses five cases. A high school student can not understand their method. |
出于本能,我google了一下“万精油”,guess what? google里第一个跳出来的就是fzy在这里的题目,而下面的几个都是些于我要找的万精油没有什么关系的东西。
每周一题by 万精油: 最多跳多远? - 顶顶华闻 - [ Translate this page ] 深圳职称评定从“万精油”中解脱出来 - [ Translate this page ] 万精油公主------------- Blogcn | 中国博客网| 博客(blog ... - [ Translate this page ]
【新语丝电子文库(www.xys.org)(www.xys2.org)】 ... - [ Translate this page ]
《国风》总目录2004 - [ Translate this page ] |
I believe it is the same 万精油 who wrote the novel. And our site is really popular. :) |
欢迎光临 珍珠湾ART (http://art.zhenzhubay.com/) | Powered by Discuz! X3 |