三角形ABC,O为BC中点,过O直线交直线AB,AC于M,N若向量AB=m向量*AM,向量AC=n*向量AN,则m+n的值在这个解法上,“延长AO至A'使AO=A'O,链接A'C交MN 于M'三角形OBM 与三角形OCM'全等,BM= CM'三角形NAM 与三角形NCM'

三角形ABC,O为BC中点,过O直线交直线AB,AC于M,N若向量AB=m向量*AM,向量AC=n*向量AN,则m+n的值在这个解法上,“延长AO至A'使AO=A'O,链接A'C交MN 于M'三角形OBM 与三角形OCM'全等,BM= CM'三角形NAM 与三角形NCM'
三角形ABC,O为BC中点,过O直线交直线AB,AC于M,N若向量AB=m向量*AM,向量AC=n*向量AN,则m+n的值
在这个解法上,
“延长AO至A'使AO=A'O,链接A'C交MN 于M'
三角形OBM 与三角形OCM'全等,BM= CM'
三角形NAM 与三角形NCM'相似,
NC/AC = CM'/AM
（AN-AC）/AN = (AB-AM)/AM
n-1 = 1-m
m+n = 2
”
从（AN-AC)/AN=(AB-AM)/AM是怎么到n-1=1-m的?
我只能变成(n-1)/n=(1-m)/m

三角形ABC,O为BC中点,过O直线交直线AB,AC于M,N若向量AB=m向量*AM,向量AC=n*向量AN,则m+n的值在这个解法上,“延长AO至A'使AO=A'O,链接A'C交MN 于M'三角形OBM 与三角形OCM'全等,BM= CM'三角形NAM 与三角形NCM'
NC/AC = CM'/AM 应该是 NC/AN = CM'/AM ,
所以,(AN-AC)/AN=(AB-AM)/AM ,
即有：1 - AC/AN = AB/AM - 1 .
已知,AC/AN = n ,AB/AM = m ,
所以,1-n = m-1 ,
可得：m+n = 2 .
你出错的原因是：
把AC看作1,却把AN看作是 n ,其实应该是 1/n ；AB和AM也一样.
应该变成：[(1/n)-1]/(1/n) = [1-(1/m)]/(1/m) ,结果也是正确的.

另解
向量AO=1/2（AB+AC）
MO=AO-AM
=1/2（AB+AC）-1/m*AB
=(1/2-1/m)AB+1/2AC
同理可得
NO=AO-AN
=1/2（AB+AC）-1/n*AC
=1/2AB+(1/2-1/n)AC
MO与NO共线，由共线定理
对应系数成比例
(1/2-1/m)：1/2=1/2：(1/2-1/n)
化简可得m+n=2

Ji Gong Chang Opera


? ? \to a try, Oh Mani Mani Mani coax coax ... ... \in front of others? \\\Let me tell you! The ancient East has a messenger, a great ancient king is great, H...

全部展开

Ji Gong Chang Opera


? ? \to a try, Oh Mani Mani Mani coax coax ... ... \in front of others? \\\Let me tell you! The ancient East has a messenger, a great ancient king is great, He was extraordinarily brave thing expedition, he has the world's largest country, that is me - Genghis Khan; do not have the emperor, I am President, if you will marry me, you can get hold of his wife's dried out, if your aunt would like an official seven Aunt Pat, I want to give them the idea of holding teachers to do some Brigadier Well, your cousin cousin want to get married, I can get public housing units to them, even if Your grandparents I can get hold of them retired in paternity case of Well \? \\\I figure like Walter, my temperament, like high-built store, Alain Delon also beats the big beautiful world you are, do we both husband and wife, the number of the first heaven and on earth is entirely consistent with that of eugenics, and their offspring smart is really great, I said, Do not you often hesitate to E fairies, and we immediately registered to get married \\you try, really I did quit heart Dong Daozi dig it \an Arab, the richest to try her a coax Oh Mani Mani Mani coax ... ... \
More articles related to topics：


A rainy day outside the window and the window _1059

黑镜头正在红色政权的躯体上聚焦_2663

A yellow _4264

收起