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Re: [問題]我有問題

發表 G@ry 於 星期四 四月 05, 2007 1:39 am

tangpakchiu 寫到:#ed_op#div#ed_cl#那當為一個鈍角三角形,題目可解嗎???#ed_op#/div#ed_cl#
#ed_op#br#ed_cl#若ABC為鈍角三角形,則跟(1)的情況差不多:#ed_op#br#ed_cl##ed_op#span class="postbody"#ed_cl##ed_op#/span#ed_cl##ed_op#img src="file:///D:/DnS/%A2%D5%A2Iry/%AE%E0%AD%B1/a.GIF" alt=""#ed_cl##ed_op#img src="richedit/upload/2kf919a0fdc8.gif" alt="image file name: 2kf919a0fdc8.gif" border="0"#ed_cl##ed_op#br#ed_cl#只是BC移至比較接近A的地方而已....E、F、G也為同一點....故不可行...#ed_op#br#ed_cl##ed_op#br#ed_cl#
tangpakchiu 寫到:#ed_op#div#ed_cl#對不起....本身的題目沒有提到ABC是否為一鈍or銳角三角形....#ed_op#/div#ed_cl#
#ed_op#br#ed_cl#水落石出了....原來是加了添加劑....:P:P#ed_op#br#ed_cl##ed_op#br#ed_cl##ed_op#br#ed_cl#但原問題本來是甚麼?#ed_op#br#ed_cl#你可以只貼原來的問題嗎?...#ed_op#br#ed_cl#

[問題]我有問題

發表 tangpakchiu 於 星期三 四月 04, 2007 5:46 pm

#ed_op#DIV#ed_cl#對不起....本身的題目沒有提到ABC是否為一鈍or銳角三角形....那當為一個鈍角三角形,題目可解嗎???#ed_op#/DIV#ed_cl#

發表 MP 於 星期三 四月 04, 2007 12:44 pm

#ed_op#DIV#ed_cl#也許這是一道偽命題。#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl##ed_op#/DIV#ed_cl#

Re: [問題]你的問題

發表 G@ry 於 星期三 四月 04, 2007 1:16 am

tangpakchiu 寫到:#ed_op#div#ed_cl#i am sorry for that....#ed_op#/div#ed_cl##ed_op#div#ed_cl# #ed_op#/div#ed_cl##ed_op#div#ed_cl##ed_op#span class="postbody"#ed_cl##ed_op#font size="2"#ed_cl# #ed_op#/font#ed_cl##ed_op#div#ed_cl##ed_op#font size="2"#ed_cl##ed_op#img alt="image file name: 2kb14e58bfb5.gif" src="http://yll.loxa.edu.tw/phpBB2/richedit/upload/2kb14e58bfb5.gif" border="0"#ed_cl##ed_op#/font#ed_cl##ed_op#/div#ed_cl##ed_op#div#ed_cl#ABC為一銳角三角形,E為角A的角平分線,G為BC的中點,A、B、D、C共圓,求證AD是A、B、D、C外接圓的直徑。#ed_op#/div#ed_cl##ed_op#/span#ed_cl##ed_op#/div#ed_cl#
#ed_op#br#ed_cl#其實小弟很懷疑ABC是否為銳角三角形,因為銳角三角形的定義是三個角皆小於90#ed_op#sup#ed_cl#o#ed_op#/sup#ed_cl# 。#ed_op#br#ed_cl##ed_op#br#ed_cl#若AD是外接圓的直徑,由於BG=GC,故有以下三種可能:#ed_op#br#ed_cl#1.#ed_op#br#ed_cl##ed_op#img src="richedit/upload/2kcfd3e4b1be.gif" alt="image file name: 2kcfd3e4b1be.gif" border="0"#ed_cl##ed_op#br#ed_cl##ed_op#span id="convert155999"#ed_cl##ed_op#span class="postbody"#ed_cl#Δ#ed_op#/span#ed_cl##ed_op#/span#ed_cl#ABC的確為銳角三角形,但BG與AD垂直,使E、F、G為同一點... (好像與題目的圖不同....)#ed_op#br#ed_cl##ed_op#br#ed_cl#2.#ed_op#br#ed_cl##ed_op#img src="richedit/upload/2k084620e63c.gif" alt="image file name: 2k084620e63c.gif" border="0"#ed_cl##ed_op#br#ed_cl#這個完全符合題目的圖,但由於BG=GC,BC為外接圓ABDC的另一直徑,故#ed_op#span id="convert155999"#ed_cl##ed_op#span class="postbody"#ed_cl#∠CAB=90#ed_op#sup#ed_cl#o#ed_op#/sup#ed_cl#,#ed_op#/span#ed_cl##ed_op#/span#ed_cl##ed_op#span id="convert155999"#ed_cl##ed_op#span class="postbody"#ed_cl#Δ#ed_op#/span#ed_cl##ed_op#/span#ed_cl##ed_op#span id="convert155999"#ed_cl##ed_op#span class="postbody"#ed_cl#ABC為直角三角形而非銳角三角形....#ed_op#/span#ed_cl##ed_op#/span#ed_cl#(有一角不少於90#ed_op#sup#ed_cl#o#ed_op#/sup#ed_cl#)#ed_op#br#ed_cl##ed_op#br#ed_cl#3.#ed_op#br#ed_cl##ed_op#img src="richedit/upload/2k4dd23de57e.gif" alt="image file name: 2k4dd23de57e.gif" border="0"#ed_cl##ed_op#br#ed_cl#這個...跟2相似....但EFG位置全部轉置了,而且#ed_op#span id="convert155999"#ed_cl##ed_op#span class="postbody"#ed_cl##ed_op#/span#ed_cl##ed_op#/span#ed_cl##ed_op#span id="convert155999"#ed_cl##ed_op#span class="postbody"#ed_cl#Δ#ed_op#/span#ed_cl##ed_op#/span#ed_cl##ed_op#span id="convert155999"#ed_cl##ed_op#span class="postbody"#ed_cl#ABC跟2一樣為直角三角形....太胡扯了吧....#ed_op#br#ed_cl##ed_op#br#ed_cl#其實還有第四種可能,就是集合了1,2,3各可能出現的問題之大成:#ed_op#br#ed_cl##ed_op#/span#ed_cl##ed_op#/span#ed_cl##ed_op#img src="richedit/upload/2ka7d5fec361.gif" alt="image file name: 2ka7d5fec361.gif" border="0"#ed_cl##ed_op#br#ed_cl##ed_op#span id="convert155999"#ed_cl##ed_op#span class="postbody"#ed_cl#這個....超級無敵大胡扯....沒可能吧...#ed_op#br#ed_cl##ed_op#/span#ed_cl##ed_op#/span#ed_cl##ed_op#br#ed_cl##ed_op#br#ed_cl#是故小弟猜想題目為:"#ed_op#span id="convert155999"#ed_cl##ed_op#span class="postbody"#ed_cl#Δ#ed_op#/span#ed_cl##ed_op#/span#ed_cl##ed_op#span id="convert155999"#ed_cl##ed_op#span class="postbody"#ed_cl#ABC為非鈍角三角形..." 而非現在的"銳角三角形"....#ed_op#/span#ed_cl##ed_op#/span#ed_cl##ed_op#span id="convert155999"#ed_cl##ed_op#span class="postbody"#ed_cl##ed_op#br#ed_cl#否則,此題為不可證也。#ed_op#br#ed_cl##ed_op#/span#ed_cl##ed_op#/span#ed_cl#

[問題]你的問題

發表 tangpakchiu 於 星期二 四月 03, 2007 9:03 pm

#ed_op#DIV#ed_cl#i am sorry for that....#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl# #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl##ed_op#SPAN class=postbody#ed_cl##ed_op#FONT size=2#ed_cl# #ed_op#/FONT#ed_cl##ed_op#DIV#ed_cl##ed_op#FONT size=2#ed_cl##ed_op#IMG alt="image file name: 2kb14e58bfb5.gif" src="http://yll.loxa.edu.tw/phpBB2/richedit/upload/2kb14e58bfb5.gif" border=0#ed_cl##ed_op#/FONT#ed_cl##ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#ABC為一銳角三角形,E為角A的角平分線,G為BC的中點,A、B、D、C共圓,求證AD是A、B、D、C外接圓的直徑。#ed_op#/DIV#ed_cl##ed_op#/SPAN#ed_cl##ed_op#/DIV#ed_cl#

Re: [問題]幾何題56

發表 G@ry 於 星期二 四月 03, 2007 5:14 pm

tangpakchiu 寫到:#ed_op#div#ed_cl##ed_op#img alt="image file name: 2kb14e58bfb5.gif" src="http://yll.loxa.edu.tw/phpBB2/richedit/upload/2kb14e58bfb5.gif" border="0"#ed_cl##ed_op#/div#ed_cl##ed_op#div#ed_cl#ABC為一銳角三角形,E為角A的角平分線,G為BC的中點,A、B、D、C共圓,角BAF=角DAC,求證AD是A、B、D、C外接圓的直徑。#ed_op#/div#ed_cl#
#ed_op#br#ed_cl#...不好意思...這個圖怎看也是像鈍角三角形多些.... :P:P:P#ed_op#br#ed_cl#∠BAF=∠DAC | given#ed_op#br#ed_cl#∠ABF=∠ABC=∠ADC | ABDC共圓#ed_op#br#ed_cl#∴ΔABF~#ed_op#img src="file:///D:/Temp/moz-screenshot.jpg" alt=""#ed_cl#ΔADC | 兩角相等#ed_op#br#ed_cl#∠ACD=∠AFB=90#ed_op#sup#ed_cl#o#ed_op#/sup#ed_cl##ed_op#br#ed_cl#=> 由於ABDC共圓而∠ACD=90#ed_op#sup#ed_cl#o#ed_op#/sup#ed_cl#,AD為ABDC外接圓的直徑。#ed_op#br#ed_cl##ed_op#br#ed_cl#p.s. 此題是不是有下文的?...E, G點及銳角的特質也沒有用過....#ed_op#br#ed_cl#

[問題]幾何題56

發表 tangpakchiu 於 星期二 四月 03, 2007 1:52 pm

#ed_op#DIV#ed_cl##ed_op#IMG alt="image file name: 2kb14e58bfb5.gif" src="http://yll.loxa.edu.tw/phpBB2/richedit/upload/2kb14e58bfb5.gif" border=0#ed_cl##ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#ABC為一銳角三角形,E為角A的角平分線,G為BC的中點,A、B、D、C共圓,角BAF=角DAC,求證AD是A、B、D、C外接圓的直徑。#ed_op#/DIV#ed_cl#