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It is known that a, B and C are the three sides of triangle ABC, and the square of a + the square of 2B + the square of C is equal to 2B (a + C) It is known that a, B and C are the three sides of triangle ABC, and the square of a + the square of 2B + the square of C is equal to 2B (a + C). Try to judge the shape of triangle ABC and explain the reason
a^2+2b^2+c^2-2b(a+c)=a^2+b^2-2ab+b^2+c^2-2bc
=(a-b)^2+(b-c)^2=0
So A-B = 0, B-C = 0
So a = b = C is an equilateral triangle
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