# 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 $$a + b$$.

×