Concentric Circles Equally Split This Chord

Geometry Level 5

Let [A][A] denote the area of circle AA. Suppose that 1010 concentric circles O1,O2,,O10O_1,O_2,\ldots,O_{10} satisfy [Oi]>[Oi+1][O_i] > [O_{i+1}] for all i=19i=1\to 9. Also, a chord drawn in circle O1O_1 has the property that circles O2O10O_2\to O_{10} cut it into 1919 equal sections. The chord has length 20142014, and [O1]+[O2]+[O3]++[O10]<20140000[O_1]+[O_2]+[O_3]+\cdots +[O_{10}]<20140000

What is the largest possible integer value of the radius of O10O_{10}?

You are permitted to use a scientific calculator.

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