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Geometry Difficulty 3.0 AMC 10/12 Find the answer United Kingdom

The points $P(d, -d)$ and $Q(12-d, 2d-6)$ both lie on the circumference of the same circle whose centre is the origin. What is the sum of the two possible values of $d$ ?

(A) $-16$ (B) $-4$ (C) $4$ (D) $8$ (E) $16$

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