# Ratio problem.

Level pending

Let $$ABC$$ be an equilateral triangle with side length $$a$$.Let $$P$$ be a point inside this triangle and let $$D$$ , $$E$$ and $$F$$ be the foots of the perpendiculars from $$P$$ to $$AB$$, $$BC$$ and $$AC$$.If $$\dfrac{PD+PE+PF}{3a}=k$$ then what is $$12k^2$$?

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