MathNet 2007-part-03 — 185 problems (EN–VI) Question 75

Points $A$, $B$, and $C$ lie in that order on line $\ell$, such that $AB = 3$ and $BC = 2$. Point $H$ is such that $CH$ is perpendicular to $\ell$. Determine the length $CH$ such that $\angle AHB$ is as large as possible.