# JOMO 7, Short 9

Geometry Level 5

Let $$I$$ be the incenter of $$\triangle ABC$$, 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 $$\dfrac{ID}{IF} =\dfrac{a}{b}$$ for positive, co-prime integers $$a$$ and $$b$$ Find the value of $$a+b$$.

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