# Weird Ratio

Geometry Level 3

In $$\triangle{ABC}$$, Let $$D$$ and $$E$$ be the trisection points of $$BC$$ with $$D$$ between $$B$$ and $$E$$. Let $$F$$ be the midpoint of $$AC$$, and let $$G$$ be the midpoint of $$AB$$. Let $$H$$ be the intersection of $$EG$$ and $$DF$$. If the ratio $$EH:HG$$ equals $$a:b$$ where $$a,b$$ are relatively prime positive integers. Find $$a+b$$.

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