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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