# Infimum And Supremum In Triangles?

Geometry Level 5

Given a non-degenerate triangle $$ABC$$ with perimeter 16 with $$A_1$$, $$B_1$$ and $$C_1$$ on $$BC$$, $$CA$$ and $$AB$$ such that $$AA_1$$, $$BB_1$$ and $$CC_1$$ are medians.

What is the sum of the infimum and supremum values of $$AA_1+BB_1+CC_1$$.

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