中三坐標圖問題

Consider one possible case as:


圖片參考：http://imgcld.yimg.com/8/n/HA00430218/o/20131017000012.jpg


2013-10-17 00:01:15 補充：
Oh, I am terribly sorry again Mr. Kwok~

When I started doing the question, I was really not aware that you are answering too.

2013-10-17 00:01:56 補充：
However, please note that

" PA² + PB² + PC² < 81 "

and

" PA + PB + PC < 9 "

are different conditions.

2013-10-17 00:20:53 補充：
哦～
原來舊帖有～～

今次郭老師也可以正式拜會彩虹師兄啦～

☆ヾ(◕‿◕)ノ　　(◕‿◕✿)

2013-10-17 03:31:37 補充：
但係個問題係咁： "p implies q" 唔代表 "q implies p"。

It is true that "PA + PB + PC < 9" implies "PA² + PB² + PC² < 81".

However,
(x,y) = (8/3,4/3) can satisfy PA² + PB² + PC² < 81.

You cannot be sure that it can satisfy PA + PB + PC < 9.

2013-10-17 03:31:50 補充：
(Actually I have checked that it is not.)

:-(

2013-10-17 03:37:42 補充：
For (x,y) = (8/3,4/3),

PA + PB + PC

= √[(8/3-1)² + (4/3-5)²] + √[(8/3-2)² + (4/3+1)²] + √[(8/3-5)² + (4/3-0)²]

= 9.141804537

> 9

是的，當初想錯了，但再想想之後發現好好彩。

PA + PB + PC < 9

PA² + PB² + PC² + 2(PAPB + PBPC + PCPA) < 81

PA² + PB² + PC² < 81

2013-10-17 02:05:19 補充：
Don't worry Masterijk, you are welcome.

2013-10-17 10:58:05 補充：
驗算貓 ：
多謝指正，真的計錯了。

所見略同
http://hk.knowledge.yahoo.com/question/question?qid=7012110900283