Maxima 5.5 Tue Dec 5 16:55:33 2000 (with enhancements by W. Schelter).
Licensed under the GNU Public License (see file COPYING)
(C1) eq1:a^2+(b-1)^2+(b-a)^2=4*a^2;
                           2          2    2      2
(D1)                (b - a)  + (b - 1)  + a  = 4 a
(C2) eq2:2*(a-c)^2+(c-1)^2=4*a^2;
                           2            2      2
(D2)                (C - 1)  + 2 (a - C)  = 4 a
(C3) eq3:c^2+2*(b-c)^2=4*a^2;
                         2            2      2
(D3)                    C  + 2 (b - C)  = 4 a
(C4) solve([eq1,eq2,eq3],[a,b,c]);
(D4) [[a = - 1.354357099329677, b = - 1.345799769850403, 

C = 0.53221512247071], [a = - 0.801953125, b = 0.49009176752228, 

C = - 0.57000486144871], [a = 0.29415855354659, b = 0.71947312210751, 

C = 0.46118546845124], [a = - 0.19731527459567 %I - 0.14684094463788, 

b = 0.48924683094491 %I + 0.40427766110958, 

C = 0.42273813184864 %I + 0.21441296879366], 

[a = 0.19731527459567 %I - 0.14684094463788, 

b = 0.40427766110958 - 0.48924683094491 %I, 

C = 0.21441296879366 - 0.42273813184864 %I], 

[a = 0.29066493393979, b = 0.67599402092676, C = 0.55601792573624]]
(C5)