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The figure below shows four mutually tangent circles O_{1}, O_{2}, O_{3}, and O_{4} so that angle O_{1}O_{2}O_{3} = 90 degrees. If radius of circle O_{1} = 4 and radius of circle O_{2} = 1, find the radius of circle O_{4}.

See Kaleidoscope of Problem 1157 base on Poincare Disk Model.

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