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Question Number 10947 by rish@bh last updated on 03/Mar/17
In a triangle ABC prove the following  (((a+b+c)^2 )/(a^2 +b^2 +c^2 )) = ((cot (A/2)+cot (B/2)+cot (C/2))/(cot A+cot B+cot C))
$$\mathrm{In}\:\mathrm{a}\:\mathrm{triangle}\:\mathrm{ABC}\:\mathrm{prove}\:\mathrm{the}\:\mathrm{following} \\ $$$$\frac{\left({a}+{b}+{c}\right)^{\mathrm{2}} }{{a}^{\mathrm{2}} +{b}^{\mathrm{2}} +{c}^{\mathrm{2}} }\:=\:\frac{\mathrm{cot}\:\frac{{A}}{\mathrm{2}}+\mathrm{cot}\:\frac{{B}}{\mathrm{2}}+\mathrm{cot}\:\frac{{C}}{\mathrm{2}}}{\mathrm{cot}\:{A}+\mathrm{cot}\:{B}+\mathrm{cot}\:{C}} \\ $$

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