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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