Question 1
Let $ABCD$ be a quadrilateral circumscribed about a circle, whose interior and exterior angles are at least $60$ degrees. Prove that
$$\frac13|AB^3-AD^3|\le|BC^3-CD^3|\le3|AB^3-AD^3|.$$
When does equality hold?
Proposed by Titu Andreescu (credited in the supplied source).
$$\frac13|AB^3-AD^3|\le|BC^3-CD^3|\le3|AB^3-AD^3|.$$
When does equality hold?
Proposed by Titu Andreescu (credited in the supplied source).