Question 144
Let $ABCD$ be a quadrilateral circumscribed about a circle, whose interior and exterior angles are at least $60^{\circ}$. Prove that
$$
\frac{1}{3} |AB^3 - AD^3| \leq |BC^3 - CD^3| \leq 3|AB^3 - AD^3|.
$$
When does equality hold?
$$
\frac{1}{3} |AB^3 - AD^3| \leq |BC^3 - CD^3| \leq 3|AB^3 - AD^3|.
$$
When does equality hold?