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In-ABC-prove-that-a-b-b-c-c-a-R-2-4r-2-1-b-2-a-2-c-2-b-2-a-2-c-2-




Question Number 163588 by HongKing last updated on 08/Jan/22
In  △ABC  prove that  (a/b) + (b/c) + (c/a) + (R^2 /(4r^2 )) ≥ 1 + (b^2 /a^2 ) + (c^2 /b^2 ) + (a^2 /c^2 )
$${In}\:\:\bigtriangleup{ABC}\:\:{prove}\:{that} \\ $$$$\frac{{a}}{{b}}\:+\:\frac{{b}}{{c}}\:+\:\frac{{c}}{{a}}\:+\:\frac{{R}^{\mathrm{2}} }{\mathrm{4}{r}^{\mathrm{2}} }\:\geqslant\:\mathrm{1}\:+\:\frac{{b}^{\mathrm{2}} }{{a}^{\mathrm{2}} }\:+\:\frac{{c}^{\mathrm{2}} }{{b}^{\mathrm{2}} }\:+\:\frac{{a}^{\mathrm{2}} }{{c}^{\mathrm{2}} } \\ $$

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