# 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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