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if-point-P-is-any-point-inside-ABC-with-side-lenghts-a-b-and-c-prove-that-PA-a-PB-b-PC-c-3-




Question Number 187762 by normans last updated on 21/Feb/23
        if point P  is any point inside            △ABC  with side lenghts a,b and c.               prove that;                    ((PA)/a) + ((PB)/b) + ((PC)/c) ≥ (√(3 ))
$$ \\ $$$$\:\:\:\:\:\:\boldsymbol{{if}}\:\boldsymbol{{point}}\:\boldsymbol{{P}}\:\:\boldsymbol{{is}}\:\boldsymbol{{any}}\:\boldsymbol{{point}}\:\boldsymbol{{inside}}\:\:\: \\ $$$$\:\:\:\:\:\:\:\bigtriangleup\boldsymbol{{ABC}}\:\:\boldsymbol{{with}}\:\boldsymbol{{side}}\:\boldsymbol{{lenghts}}\:\boldsymbol{{a}},\boldsymbol{{b}}\:\boldsymbol{{and}}\:\boldsymbol{{c}}.\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\boldsymbol{{prove}}\:\boldsymbol{{that}}; \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\frac{\boldsymbol{{PA}}}{\boldsymbol{{a}}}\:+\:\frac{\boldsymbol{{PB}}}{\boldsymbol{{b}}}\:+\:\frac{\boldsymbol{{PC}}}{\boldsymbol{{c}}}\:\geqslant\:\sqrt{\mathrm{3}\:} \\ $$$$ \\ $$

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