Those are fine circles!

Geometry Level 4

A circumcentre \( O_{1} \) of the first circle of radius \( r \), is located on a circumference of the second circle of radius \( 2r \) (\( O_{2} \) is its circumcentre). Points \( A \) and \( B \) are common points of circumferences. Segments \( AB \) and \( O_{2}O_{1} \) intercept in point \( X \). An appropriate image of all this is provided above.

If \( \frac{O_{2}X}{O_{2}O_{1}} = \frac{a}{b} \), where \( a \) and \( b \) are coprime positive integers, find \( a + b \).

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