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x-C-h-2-3-s-2-x-C-2-a-2-x-A-h-2-3-s-2-x-A-2-c-2-x-C-x-A-2-b-2-4-




Question Number 56264 by ajfour last updated on 13/Mar/19
(x_C −h)^2 +3((s/2)−x_C )^2  = a^2    (x_A −h)^2 +3((s/2)+x_A )^2 = c^2     (x_C −x_A )^2  = b^2 /4 .
$$\left({x}_{{C}} −{h}\right)^{\mathrm{2}} +\mathrm{3}\left(\frac{{s}}{\mathrm{2}}−{x}_{{C}} \right)^{\mathrm{2}} \:=\:{a}^{\mathrm{2}} \\ $$$$\:\left({x}_{{A}} −{h}\right)^{\mathrm{2}} +\mathrm{3}\left(\frac{{s}}{\mathrm{2}}+{x}_{{A}} \right)^{\mathrm{2}} =\:{c}^{\mathrm{2}} \\ $$$$\:\:\left({x}_{{C}} −{x}_{{A}} \right)^{\mathrm{2}} \:=\:{b}^{\mathrm{2}} /\mathrm{4}\:. \\ $$
Commented by MJS last updated on 12/Mar/19
seems impossible
$$\mathrm{seems}\:\mathrm{impossible} \\ $$
Commented by ajfour last updated on 13/Mar/19
Commented by ajfour last updated on 13/Mar/19
Find maximum and minimum  value of edge length s of  circumscribing equilateral △.
$${Find}\:{maximum}\:{and}\:{minimum} \\ $$$${value}\:{of}\:{edge}\:{length}\:{s}\:{of} \\ $$$${circumscribing}\:{equilateral}\:\bigtriangleup. \\ $$

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