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MathNet 2008-part-01 — 165 problems (EN–VI) Question 66

Math Olympiad Vault · MathNet 2008-part-01 — 165 problems (EN–VI)

Question 66

In a circle of diameter $1$, some chords are drawn. The sum of their lengths is greater than $19$. Prove that there is a diameter intersecting at least $7$ chords.