Concentric Circles Equally Split This Chord

Geometry Level 5

Let \([A]\) denote the area of circle \(A\). Suppose that \(10\) concentric circles \(O_1,O_2,\ldots,O_{10}\) satisfy \([O_i] > [O_{i+1}]\) for all \(i=1\to 9\). Also, a chord drawn in circle \(O_1\) has the property that circles \(O_2\to O_{10}\) cut it into \(19\) equal sections. The chord has length \(2014\), and \[[O_1]+[O_2]+[O_3]+\cdots +[O_{10}]<20140000\]

What is the largest possible integer value of the radius of \(O_{10}\)?

You are permitted to use a scientific calculator.

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