MathNet 2023-part-02 — 191 problems (EN–VI) Question 143

$ABCD$ is a square of side length $1$. $BC$ is extended to $E$ and $DC$ is extended to $F$ such that $BE = DF = 3$. The circumcircle of $\triangle AEF$ meets the extensions of $CB$ and $CD$ at $G$ and $H$ respectively. Find $GH$.