s = ((a + b + c)/2);
S = (Sqrt[s (s - a) (s - b) (s - c)]);
R = ((a b c)/(4 S));
ma = (1/2) (Sqrt[2  (b^2) + 2  (c^2) - (a^2)]);

Factor[(a^4) - 16 (R^2) (ma^2)]

a2 = 1;
b2 = (((x - 1))^2) + (y^2);
c2  = (x^2) + (y^2);
Factor[(a2^2) - a2 (b2 + c2) - 8 b2 c2]

<< Graphics`ImplicitPlot`;

curva = 
        ImplicitPlot[-x + 5 (x^2) - 8 (x^3) + 4 (x^4) + 5 (y^2) - 
              8 x (y^2) + 8 (x^2) (y^2) + 4 (y^4) == 0, {x, 0, 
            1}, {y, -0.5, 0.5}, 
          AspectRatio -> Automatic];

Show[curva, Graphics[Line[{{0, 0}, {1, 0}}]]]

Solve[-x + 5 (x^2) - 8 (x^3) + 4 (x^4) + 5 (y^2) - 8 x (y^2) + 
          8 (x^2) (y^2) + 4 (y^4) == 0, y]

sqrt(-(5/8) + a - a^2 + (1/8)*sqrt(25 - 64*a + 64*a^2))

For[a = 1, 
      a < 100, a++, 
For[b = 1, 
        b < 100, b++, 
For[c = 1, 
          c < 100, c++, 
If[
            (a^4) - (a^2) (b^2) - (a^2) (c^2) - 8 (b^2) (c^2) == 
                0   &&   a >  b + c, Print[{a, b, c}]]]]]