MathNet 2024-part-06 — 165 problems (EN–VI) Question 107

Let $ABCD$ be a trapezoid with $AB \parallel CD$. Point $X$ is placed on segment $\overline{BC}$ such that $\angle BAX = \angle XDC$. Given that $AB = 5$, $BX = 3$, $CX = 4$, and $CD = 12$, compute $AX$.