# Inspired by Calvin Lin: Any part 1

Geometry Level 4

Suppose $$AD, BE, CF$$ are the medians of a triangle $$ABC$$, with side $$BC = 10$$, intersecting at $$G$$.

In the quadrilateral $$AEGF$$, suppose $$AE\times AF = 3\times GE\times GF$$,
evaluate $$\dfrac{AB\times BE+ AC\times CF}{AD}$$.

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