YLL討論網

(1)1和2是兩種不同的證法嗎???
不是~是兩個引理，先證他們，再證題目
(2)2中所指的兩個相似三角形是什麼???
AO2C和CO1D
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Sorry~塗鴉中的圓心標反了

#ed_op#DIV#ed_cl#現在頭腦不是太清醒......#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#1和2是兩種不同的證法嗎???#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#2中所指的兩個相似三角形是什麼???#ed_op#/DIV#ed_cl#

1.角ACB=90度
證：作內公切線交AB於M，因為外公切線等長，所以MA=MB=MC，以M為圓心....
2.兩外切圓半徑比=過兩圓切點直線形成之兩弦比
證：借圖一用，ACD分別與圓心連線，因為半徑相等+對頂角相等得兩相似三角....
所以O1C:O2C=3:1...(1)
連接O1B,O2A，並作C點的垂線交AB於H
由(1)AH:BH=1:3
令AH=K,BH=3K
又角ACB=90度
用母子性質
CH=sqrt3*K
三角形BCH邊長比為1:sqrt3:2
故角ABC=30度

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