Side Median Ratio

Geometry Level 3

ADAD, BEBE and CFCF are the medians of the triangle ABCABC. If ADBEAD \perp BE, then ABCF\dfrac{AB}{CF} can be expressed as pq\dfrac{p}{q} where pp and qq are co-prime positive integers. What is p+qp+q?


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

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