not as easy as abcd

Algebra Level 5

Consider all ordered triplets \( (a , b , c) \) of real numbers which satisfy

\( 8a^2 + 8b^2 - c^2 = 0 . \)

Define the function \( d (a, b, c) \) such that it satisfies the equation

\( (1 -d)a^2 + (1-d)b^2 + c^2 + 2ab + 2bc + 2ac = 0 \),

Over all possible triplets, what is the minimum value of \( d(a, b, c) \)?

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