# Joining

Geometry Level 5

In triangle $$\triangle ABC$$, let $$BC=7$$, $$AC=6$$ and $$AB=5$$. Let $$D$$, $$E$$ and $$F$$ be the centers of the excircles relatives to $$BC$$, $$AC$$ and $$AB$$ respectively.

If $$EF=\dfrac{c \sqrt{a}}{g}$$, $$DF=\dfrac{d\sqrt{ab}}{g}$$ and $$DE=f\sqrt{b}$$, where $$ab$$ is square free, $$\gcd(c,g)=1$$ and $$\gcd(d,g)=1$$, find $$abc-dfg$$.

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