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Yahoo!奇摩知識+ - 分類問答 - 科學常識 - 已解決
Yahoo!奇摩知識+ - 分類問答 - 科學常識 - 已解決 
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數學題求解
Dec 15th 2013, 07:51

http://imgur.com/aSLHK0c
(開圖比較好看)
&becaus;<-這個是「因為」的意思
∴<-這個是「所以」的意思
以BC為軸,對稱ΔABC到ΔA'BC,D點到D'點
此時連AD',交BC於Q點
&becaus;AP+PD=AP+PD'(對稱)>AD'(ΔAPD'中兩邊和大於第三邊)=AQ+QD'=AQ+QD(對稱)
∴當P點重疊Q點時,AP+AD有最小值(=AQ+QD=AQ+QD'=AD')
-------------------------------------------------------------------------------------------
所以現在要求BQ(因為我們把P點重疊在Q點上,他才有最小值)
&becaus;AB=AC=A'B=A'C
∴ABCD是菱形,AB平行A'C
=>易得ΔABQ~ΔD'CQ(AA相似)
又CD'=CD(對稱)=(2/5)*AC=(2/5)*AB
∴ CQ:QB=CD':AB=2:5
又CQ+QB=CB=7
=>BQ=5,CQ=2

答:(B) 5

另外P是BC上任意一點,所以PC不一定會等於2

PS:樓上不要偷抄證明喔XDD 我先搶答的(開玩笑的)

參考資料 看過題型

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