olymmath

USAMO 2004 Problem 1

  • Day 1

Let ABCDABCD be a quadrilateral circumscribed about a circle, whose interior and exterior angles are at least 60 degrees. Prove that 13∣AB3−AD3∣≤∣BC3−CD3∣≤3∣AB3−AD3∣.\frac{1}{3}|AB^3 - AD^3| \le |BC^3 - CD^3| \le 3|AB^3 - AD^3|. When does equality hold?

Dataset text AI-MO AoPS. Quoted with source.

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