Funky Quadrilaterals

Geometry Level 5

As shown in the figure above, \(ABCD\) is a quadrilateral inscribed in a circle, and \(P\) is the intersection of its diagonals \(AC\) and \(BD.\)

Now, \(DB\) is extended to \(F\) such that \(AF\parallel DC.\)
Similarly, \(AC\) is extended to \(E\) such that \(DE\parallel AB.\)

If \(DP=18, PB=8,\) and \(BF=10,\) find the value of \(AF\times DE+AD\times FE.\)

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