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MathNet 2019-part-05 — 184 problems (EN–VI) Question 40

Math Olympiad Vault · MathNet 2019-part-05 — 184 problems (EN–VI)

Question 40

Around point $O$ one considers the angles $\widehat{A_0OA_1} = 1^\circ$, $\widehat{A_1OA_2} = 2^\circ$, $\widehat{A_2OA_3} = 3^\circ, \dots, \widehat{A_{25}OA_{26}} = 26^\circ$ and $\widehat{A_{26}OA_0}$.

a) Determine the measure of $\widehat{A_{26}OA_0}$.

b) For what integers $n$, such that $1 \le n \le 25$, one has $\widehat{A_0OA_n} \gt \widehat{A_0OA_{n+1}}$?