# Area Inside an Obtuse Triangle

Geometry Level 4

Triangle $$ABC$$ has an obtuse angle at $$B$$, base $$BC$$ has length equal to $$30$$ and height equal to $$24$$. (This height is taken with respect to base $$BC$$). $$D$$ is a point on the line segment $$BC$$ and $$E$$ is a point on $$AC$$ such that $$DE \parallel AB$$. $$F$$ is a point on $$AB$$ such that $$FD \parallel AC$$. As $$D$$ varies within line segment $$BC$$, what is the maximum value of $$[DEF]$$?

Details and assumptions

$$[PQRS]$$ denotes the area of the figure $$PQRS$$.

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