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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