Intersection of Three Chords

Geometry Level 3

On the circumference of circle $\Gamma$ , chord $AB$ with length $1100$ is drawn. Let $C$ be the midpoint of $AB$ . Through $C$ , 2 other chords $DE$ and $FG$ are also drawn, such that the points around the circle are $A, D, F, B, E, G$ . The line segment $AB$ intersects $DG$ and $FE$ (internally) at $H$ and $I$ , respectively.

If $AH=449$ , what is $CI?$