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MathNet 2023-part-07 — 187 problems (EN–VI) Question 162

Math Olympiad Vault · MathNet 2023-part-07 — 187 problems (EN–VI)

Question 162

Pentagon $S P E A K$ is inscribed in triangle $N O W$ such that $S$ and $P$ lie on segment $N O$, $K$ and $A$ lie on segment $N W$, and $E$ lies on segment $O W$. Suppose that $N S = S P = P O$ and $N K = K A = A W$. Given that $E P = E K = 5$ and $E A = E S = 6$, compute $O W$.