Length of AC makes me cry!!!???

Geometry Level 5

Let \(I\) be the incenter of a triangle \(ABC\) and let\(AI,BI\) and \( CI\) intersect \(BC,CA\) and AB at \(D,E\) and F respectively. If \(AB=20\),\(BC=14\) and \(AC=\frac{438}{53}\), then \(\frac{ID}{IF}\)=\(\frac{a}{b}\) for positive coprime integers \(a\) and \(b\). Find the value of \(a+b\).

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