Playing with circles

Geometry Level pending

Consider two circles \(S\) and \(R\). Let the center of circle \(S\) lie on \(R\). Let \(S\) and \(R\) intersect at \(A\) and \(B\). Let \(C\) be a point on \(S\) such that \(AB=AC\). Then must the point of intersection of \(AC\) and \(R\) lie in \(S\)?

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