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3.設△ABC 中，  ，∠A 的內角平分線交  於 D， 邊上的高為  ，且   交 於P，若  ，則數對α + β =？
(A) 7/9
(B) 5/9
(C)2/3
(D)4/9

答案：登入後觀看
難度： 困難

10
 【站僕】摩檸Morning：有沒有達人來解釋一下?
倒數 17時 ,已有 2 則答案
寫題慢錯了嗎 小一上 (2021/06/23):

先備知識:

1.畢氏定理

2.向量分點公式:

H P C在同在上4828803-6261bda758dac.jpg#s-53,42%23s-53,42%23s-53,42，且4828803-6261bda8159e6.jpg#s-54,36%23s-54,36%23s-54,36:4828803-6261bda8c77ae.jpg#s-54,39%23s-54,39%23s-54,39%23s-54,39=m : n

則4828803-6261bda98619d.jpg#s-390,80

圖示:

60d2daa7762b0.jpg#s-463,430

解題開始:

4828803-6261bdaa46859.jpg#s-373,47
利用畢氏定理: 


4828803-6261bda758dac.jpg#s-53,42%23s-53,42%23s-53,422= 42-x2 =(4828803-6261bdabbbaf3.jpg#s-59,41)2- (6-X)2

==>求得X=2 


=>4828803-6261bdac7922e.jpg#s-64,50%23s-64,50%23s-64,50%23s-64,50%23s-64,50=2，4828803-6261bdad3bcc6.jpg#s-56,46%23s-56,46%23s-56,46=4，4828803-6261bda758dac.jpg#s-53,42%23s-53,42%23s-53,42=24828803-6261bdaeae3e4.jpg#s-36,37%23s-36,37%23s-36,37

=>三角形AHC為(30度-60度-90度) 三角形
=>角BAC為60度
=>角BAP為30度(因為4828803-6261bdaf6d67e.jpg#s-68,45為角平分線)

=>三角形AHP也為(30度-60度-90度) 三角形

=>4828803-6261bda8c77ae.jpg#s-54,39%23s-54,39%23s-54,39%23s-54,39:4828803-6261bdac7922e.jpg#s-64,50%23s-64,50%23s-64,50%23s-64,50%23s-64,50:4828803-6261bdb19c340.jpg#s-46,39=1:4828803-6261bdaeae3e4.jpg#s-36,37%23s-36,37%23s-36,37:2

=>已知4828803-6261bdac7922e.jpg#s-64,50%23s-64,50%23s-64,50%23s-64,50%23s-64,50=2    =>4828803-6261bda8c77ae.jpg#s-54,39%23s-54,39%23s-54,39%23s-54,39=4828803-6261bdb48ae97.jpg#s-141,75 

=>4828803-6261bda8159e6.jpg#s-54,36%23s-54,36%23s-54,36=24828803-6261bdaeae3e4.jpg#s-36,37%23s-36,37%23s-36,37 -4828803-6261bdb6bdcb5.jpg#s-61,70%23s-61,70 =4828803-6261bdb77b5fc.jpg#s-77,67%23s-77,67

=>4828803-6261bda8c77ae.jpg#s-54,39%23s-54,39%23s-54,39%23s-54,39:4828803-6261bda8159e6.jpg#s-54,36%23s-54,36%23s-54,36=4828803-6261bdb6bdcb5.jpg#s-61,70%23s-61,70 :4828803-6261bdb77b5fc.jpg#s-77,67%23s-77,67=1:2 且H P C在同一線上

=>4828803-6261bdbb28291.jpg#s-261,84(向量分點公式)

=>因為4828803-6261bdac7922e.jpg#s-64,50%23s-64,50%23s-64,50%23s-64,50%23s-64,50=2，4828803-6261bdad3bcc6.jpg#s-56,46%23s-56,46%23s-56,46=4，4828803-6261bdac7922e.jpg#s-64,50%23s-64,50%23s-64,50%23s-64,50%23s-64,50:4828803-6261bdad3bcc6.jpg#s-56,46%23s-56,46%23s-56,46=1:2

=>4828803-6261bdbeceec0.jpg#s-136,53

所以:

4828803-6261bdbf8e6e1.jpg#s-264,250

=>   α + β =4828803-6261bdc053356.jpg#s-18,54+4828803-6261bdc113153.jpg#s-14,57=4828803-6261bdc1c652e.jpg#s-46,89

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weiluther (2022/09/22):
632c74acefd70.jpg
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3.設△ABC 中，  ，∠A 的內角平分線交  於 D， ..-阿摩線上測驗