设万维读者为首页 广告服务 技术服务 联系我们 关于万维
简体 繁体 手机版
分类广告
版主:侠行天涯
万维读者网 > 灵机一动 > 帖子
我也做出来了,不漂亮,不简洁。
送交者: 零加一中 2016年12月12日12:48:02 于 [灵机一动] 发送悄悄话

为避免打字中大量中英文切换,我用英文写出。

We first state a theorem. In ∆ABC, if AD (D on BC) bisects A, then AB/AC = AD/CD.

Our problem is this. In ∆ABC, AD and AE trisect A. Here D and E are on BC with the order from left B, D, E, and C. Is it possible that BD = 1, DE = 2, and EC = 4?

BAD = DAE = EAC = a (Given).

AE/AB = 2, AC/AD = 2 (Apply theorem).

Take E’ on AE so that ADE' = ABD.

We get immediately

∆ABD ~ ∆ADE'

 Here “~” means similar (may not be same).

ADE = ABD + a (exterior of ∆ABD).

Because ADE' = ABD,

E’DE = ADE – ADE’ = a.

Look at ∆ABD and ∆DE’E. DAE = E’DE =a. They both have AED.

∆ADE ~ ∆DE'E.

AE/DE = DE/E’E è EE’ = (DE)^2/AE = 4/AE.

Using ∆ABD ~ ∆ADE', we have

EE’ = AE – AE’ = AE – (AD)^2/AB.

Eliminating EE’, using AE/AB = 2,

4 = (AE)^2 – 2(AD)^2.

Similarly, working on ∆ADE and ∆AEC,

16 = (AC)^2 – 2(AE)^2.

Eliminating AE, we have

24 = (AC)^2 – 4(AD)^2 = 0.

原来以为我哪儿出错了,看来确实无解。

0%(0)
0%(0)
标 题 (必选项):
内 容 (选填项):
实用资讯
发龙药业大回馈!美国专利骨胶原、活心素、灯盏素、排毒养颜宝购买两疗程免费邮寄中国
天天养生,保健礼品,物超所值,疯狂现金折扣,直销美加,港台,大陆,东南亚
最劲爆,最给力美国专利产品<骨精华>消除关节痛、骨质疏松<心血通>预防心肌梗塞
免开通费,30天免费试用中文电视万花筒, 无捆绑服务,月费5.99
西洋参、羊胎盘、鱼油卵磷脂200多种送礼自用健康佳品,全部特价!由此进入
留美学生医疗保险$39/月,短期访美旅游保险,不需体检无年龄限制
一周点击热帖 更多>>
一周回复热帖
历史上的今天:回复热帖
2012: 车五进二:排队问题解答
2012: 零加一中:工作分工问题
2011: 有一种爱叫做放手,你真的放的开么?