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222-9+11+12:2*14+14 = ? ( )

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.​

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.​

Comments ( 1 )

  1. \(\begin{array}{l}
    \quad \dfrac{MH}{AM} + \dfrac{NH}{CN} + \dfrac{HK}{BK}\\
    = \dfrac{\dfrac12MH.BC}{\dfrac12AM.BC} + \dfrac{\dfrac12NH.AB}{\dfrac12CN.AB} + \dfrac{\dfrac12HK.AC}{\dfrac12BK.AC}\\
    = \dfrac{S_{BHC}}{S_{ABC}} + \dfrac{S_{AHB}}{S_{ABC}} + \dfrac{S_{AHC}}{S_{ABC}}\\
    = \dfrac{S_{BHC}+ S_{AHB}+S_{AHC}}{S_{ABC}}\\
    = \dfrac{S_{ABC}}{S_{ABC}}\\
    = 1
    \end{array}\)

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222-9+11+12:2*14+14 = ? ( )

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