Question 27
Given a circle $\omega$ and two points $A, B$ outside $\omega$. A quadrilateral inscribed in $\omega$ is called "good" if one pair of opposite sides intersects at $A$ and the other pair intersects at $B$.
Assume that at least one good quadrilateral exists. Prove that there exists a good quadrilateral $\Gamma$ such that every other good quadrilateral has area smaller than $\Gamma$.
Assume that at least one good quadrilateral exists. Prove that there exists a good quadrilateral $\Gamma$ such that every other good quadrilateral has area smaller than $\Gamma$.