Circle Radius From End Piece Measurements

Geometry Level 3

A piece of a circle was cut off along a chord of length \(B=2\). The greatest perpendicular distance from the chord to the circular arc is \(A=\dfrac{1}{3}\). The radius of the parent circle can be expressed as \(\dfrac{X}{Y}\), where \(X\) and \(Y\), where \(X\) and \(Y\) are coprime positive integers. What is the sum of \(X\) and \(Y\)?

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