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MathNet 2015-part-06 — 191 problems (EN–VI) Question 60

Math Olympiad Vault · MathNet 2015-part-06 — 191 problems (EN–VI)

Question 60

Points $A_1$, $A_2$, $A_3$ ... are constructed as follows: the length $OA_1$ is $4$, $\angle OA_1A_2 = 90^\circ$ and the length $A_1A_2 = 1$; then a right angle is constructed at $A_2$ to find $A_3$, and so on as shown in the diagram.
The length of $OA_{21}$ is

Question illustration