MathNet 2015-part-03 — 191 problems (EN–VI) Question 46

Let $ABCD$ be a square of side length $1234$. $E$ is a point on $CD$ such that $CEFG$ is a square of side length $567$ with $F$, $G$ outside $ABCD$. The circumcircle of $\triangle ACF$ meets $BC$ again at $H$. Find $CH$.