Toán hình 9

C

cuong131hv

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L

lp_qt

$\dfrac{AM}{OM}=\dfrac{S_{ABM}}{S_{ OBM}}=\dfrac{S_{AMC}}{S_{OMC}}=\dfrac{S_{ABC}}{S_{OBC}}$

tương tự:

$\dfrac{ON}{BN}=\dfrac{S_{ABC}}{S_{AOC}}$

$\dfrac{OP}{PC}=\dfrac{S_{ABC}}{S_{ABO}}$

\Rightarrow $\dfrac{AM}{OM}+\dfrac{ON}{BN}+\dfrac{OP}{PC}$

$=S_{ABC}.(\dfrac{1}{S_{AOC}}+\dfrac{1}{S_{BOC}}+ \dfrac{1}{S_{AOB}}) \ge 9$

\Rightarrow đpcm
 
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