# Random Circles

Geometry Level 4

Jane is at the center of a circle. She moves $$4\sqrt{3}$$ meters in a random direction, to a point which is still in the circle. Then, she chooses another random direction, and moves another $$4\sqrt{3}$$ meters in that direction. Given that the probability that she is now outside of the circle is $$1/3$$, what is the radius of the circle?

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