Perpendiculars from P

Geometry Level 3

An equilateral triangle ABCABC has AB=203AB = 20\sqrt{3}. PP is a point placed in triangle ABCABC and D,ED, E and FF are the foot of the perpendiculars from PP to ABAB, BCBC and ACAC, respectively. If PD=9PD = 9 and PE=10PE = 10, what is the value of the length of PFPF?

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