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![](https://rs.olm.vn/images/avt/0.png?1311)
a) Tính BM/CN ?
*tgiác DMB đồng dạng tgiác DNC
=> BM/CN = DB/DC (1)
*Do tính chất của phân giác ta có:
DB/DC = AB/AC = 24/28 = 6/7 (2)
Từ (1) và (2): BM/CN = 6/7
b)cm AM/AN = DM/DN ?
*gt: góc BAD = góc DAC
=> tgiác AMB đồng dạng tgiác ANC
=> AM/AN = AB/AC (3)
*mà ta biết tgiác DMB đồng dạng tgiác DNC
=> DM/DN = DB/DC
do(2) => DM/DN = AB/AC (4)
*Từ (3) và (4) => AM/AN = DM/DN
![](https://rs.olm.vn/images/avt/0.png?1311)
a) Xét tứ giác BHMK có 3 góc vuông nên nó là hình chữ nhật.
Khi đó hai đường chéo bằng nhau nên BM = HK.
b) Xét tam giác ABC có M là trung điểm AC, MK // AB nên MK là đường trung bình.
Vậy thì K là trung điểm BC.
Xét tứ giác BMCN có K là trung điểm hai đường chéo nên nó là hình bình hành.
Lại có MN vuông góc BC nên BMCN là hình thoi.
Dễ thấy rằng MK = AB/2 hay MN = AB.
Để hình thoi BMCN là hình vuông thì MN = BC hau AB = BC.
Vậy tam giác ABC là tam giác vuông cân tại B thì BMCN là hình vuông.
c) Ta có BHMK là hình chữ nhật nên BM giao HK tại trung điểm mỗi đường.
Dễ thấy tứ giác ABNM có AB song song và bằng NM nên nó là hình bình hành.
Vậy nên BM giao AM tại trung điểm mỗi đoạn.
Từ đó ta có BM, HK, AN đồng quy tại trung điểm mỗi đoạn.
d) Gọi giao điểm của BM, HK và AN làO, giao của BM và AK là I.
Ta có: do KM // AB, áp dụng Talet:
\(\frac{IM}{BI}=\frac{MK}{AB}=\frac{1}{2}\Rightarrow\frac{IM}{BO+OI}=\frac{1}{2}\Rightarrow\frac{IM}{IM+OI+OI}=\frac{1}{2}\)
\(\Rightarrow IM=2OM\)
Áp dụng Talet cho tam giác AND và ADC ta có:
\(\frac{OI}{DN}=\frac{AI}{AD}=\frac{IM}{DC}\Rightarrow\frac{OI}{DN}=\frac{IM}{DC}\Rightarrow DC=2ND\)
Lời giải:
Áp dụng định lý Menelaus cho tam giác $CNB$ có $A,M,D$ thẳng hàng:
$\frac{DC}{DB}.\frac{MN}{MC}.\frac{AB}{AN}=1$
Mà $M$ là trung điểm $CN$ nên $MM=MC$
$\Rightarrow \frac{DC}{DB}.\frac{AB}{AN}=1$
$\Leftrightarrow \frac{AB}{AN}=\frac{DB}{DC}$ (đpcm)
Hình vẽ:
![](data:image/png;base64,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)