The purple point

Geometry Level 4

\(\triangle ABC\) is an isosceles triangle with \(AB=AC=25\) and \(BC=14\). \(AD\) is a height from \(A\) in \(\triangle ABC\), \(E\) is the midpoint of \(AD\) and \(DF\) is a height from \(D\) in \(\triangle EDC\).

If \(\dfrac{AF}{BF}=\dfrac{a}{b}\) for coprime positive integers \(a\) and \(b\), find \(a+b\).

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