(b-c)^2=4(a-b)(c-a),
b^2-2bc+c^2=4ac-4a^2-4bc+4ab
b^2+2bc+c^2-4ac-4ab+4a^2=0
(b+c)^2-4a(b+c)+4a^2=0
(b+c-2a)^2=0
b+c-2a=0
b+c=2a