Division of area of a triangle

Geometry Level 4

\(P\) is a point in triangle \(ABC\). The lines \(AP, BP,\) and \(CP\) intersect the sides \(BC, CA,\) and \(AB\) at points \(D, E,\) and \(F\), respectively. If \( [ BDP] = 10,\) \([DPC] = 16,\) \([ APB ] = 210 \), what is \( [ APC] \)?

Details and assumptions

\( [PQRS] \) denotes the area of the figure \(PQRS\).

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