Toán Lớp 8: Cho tam giác ABC nhọn có đường cao AM; BK; CN cắt nhau tại H. Tính MH/AM + NH/CN + HK/BK.
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Toán Lớp 8: Cho tam giác ABC nhọn có đường cao AM; BK; CN cắt nhau tại H. Tính MH/AM + NH/CN + HK/BK.
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\quad \dfrac{MH}{AM} + \dfrac{NH}{CN} + \dfrac{HK}{BK}\\
= \dfrac{\dfrac12MH.BC}{\dfrac12AM.BC} + \dfrac{\dfrac12NH.AB}{\dfrac12CN.AB} + \dfrac{\dfrac12HK.AC}{\dfrac12BK.AC}\\
= \dfrac{S_{BHC}}{S_{ABC}} + \dfrac{S_{AHB}}{S_{ABC}} + \dfrac{S_{AHC}}{S_{ABC}}\\
= \dfrac{S_{BHC}+ S_{AHB}+S_{AHC}}{S_{ABC}}\\
= \dfrac{S_{ABC}}{S_{ABC}}\\
= 1
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