MathNet 2023-part-07 — 187 problems (EN–VI) Question 117

Let $A X B Y$ be a cyclic quadrilateral, and let line $A B$ and line $X Y$ intersect at $C$. Suppose $A X \cdot A Y = 6$, $B X \cdot B Y = 5$, and $C X \cdot C Y = 4$. Compute $A B^{2}$.