# 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 $CI?$

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