Playing with circles
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 \(S\)?