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Giải bài có thưởng!

Cho tam giác ABC vuông tại A, AB

cho tam giác ABC vuông tại A,AB<AC.phân giác AD.AJ vuông góc BC.DH vuông góc AB,DK vuông góc AC.BK cắt DH tại M,CHcắt DK tại N.
a)chứng minh rằng HM/MD=BH/BA
b)MN song song BC
c)gọi I là giao điểm BK và CH. chứng minh tam giác ABK đồng dạng với tam giác KAN và 3 điểm A,I,J thẳng hàng
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Tham khảo câu trả lời từ Trợ lý ảo Lazi
a) Ta có:
$\frac{HM}{MD} = \frac{HM}{BK} \cdot \frac{BK}{MD} = \frac{CH}{DK} \cdot \frac{DH}{BA} = \frac{BH}{BA}$

Vậy ta có $HM/MD=BH/BA$

b) Ta có $\angle HMD = \angle BAC = \angle BDC$ (do $ABCD$ là tứ giác nội tiếp), từ đó suy ra $MN$ song song với $BC$.

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