Trisected Triangle

Geometry Level 4

In acute triangle \(ABC\), \(O\) is an interior point. The perpendiculars from \(O\) to sides \(BC, CA\) and \(AB\) intersect the respective sides at \( D, E\) and \(F\). Given that \( FA = 12, AE =8, EC = 13\), \(CD = 11, DB = 14 \), what is the length of \( BF \)?

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