Focal Chords of an Ellipse

Geometry Level pending

Suppose \(A\), \(B\), \(C\), and \(D\) are points on an ellipse, such that segments \(AB\) and \(CD\) intersect at a focus \(F\). Given that \(AF = 3\), \(CF = 4\), and \(BF = 5\), what is \(DF\)?

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