# Side Median Ratio

Geometry Level 3

$$AD$$, $$BE$$ and $$CF$$ are the medians of the triangle $$ABC$$. If $$AD \perp BE$$, then $$\dfrac{AB}{CF}$$ can be expressed as $$\dfrac{p}{q}$$ where $$p$$ and $$q$$ are co-prime positive integers. What is $$p+q$$?

Details and assumptions: The picture isn't drawn accurately.

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