MathNet 2025 — 50 problems with figures (EN–VI) Question 36

Let $ABCD$ be a rectangle with $BC = 24$. Point $X$ lies inside the rectangle such that $\angle AXB = 90^{\circ}$. Given that triangles $\triangle AXD$ and $\triangle BXC$ are both acute and have circumradii $13$ and $15$, respectively, compute $AB$.
Proposed by: Pitchayut Saengrungkongka