# Perpendiculars from P

Geometry Level 3

An equilateral triangle $$ABC$$ has $$AB = 20\sqrt{3}$$. $$P$$ is a point placed in triangle $$ABC$$ and $$D, E$$ and $$F$$ are the foot of the perpendiculars from $$P$$ to $$AB$$, $$BC$$ and $$AC$$, respectively. If $$PD = 9$$ and $$PE = 10$$, what is the value of the length of $$PF$$?

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