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MathNet 2012 Question 12

Math Olympiad Vault · MathNet 2012

Question 12

For each positive integer $n$, there is a circle around the origin with radius $n$. Rainbow Dash starts off somewhere on the plane, but not on a circle. She takes off in some direction in a straight path. She moves $\frac{\sqrt{5}}{5}$ units before crossing a circle, then $\sqrt{5}$ units, then $\frac{3 \sqrt{5}}{5}$ units. What distance will she travel before she crosses another circle?