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\[ \large \sqrt{12+\sqrt{12+\sqrt{12+\sqrt{12 + ...}}}}= \ ? \]

In the above figure, which shaded area is larger?

The small circles all have the same size.

\[ \sqrt{ \color{purple} 2+\sqrt{ \color{purple} 2 +\sqrt{\color{purple} 2 + \cdots}}} \]

Find the radius of the circle, to 3 decimal places.

Find the minimum value of the positive integer \(x\) satisfying the inequality \[\frac{\log_{10} (2x-1)}{2}+\log_{10} \sqrt{x-9} \geq 1. \]

Source: RMO

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