A geometry problem by Christopher Boo

Geometry Level 4

A circle \[x^2+y^2-2x+4y-4=0\] intercepts line \(y=x+b\) at point \(A\) and \(B\). Given that a circle has \(AB\) as its diameter and it passes through the origin, what is the sum of all possible value of \(b\)?

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