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  • suppose that M is an arbitrary point in the triangle ABC. Through point M, construct lines DE, IJ,FG such that they are respectively parallel to BC, CA, AB ( in which G, J lie on BC; E,F lie on CA;D, I lie on AB) prove that SAIMF+SBGMD+SCEMJ\(\le\)\(\dfrac{2}{3}S_{ABC}\)

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