# 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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