# It's not completely inscribed!

Geometry Level 4

Let $$ABC$$ be an equilateral triangle. Let $$D$$ be on $$BC$$, $$E$$ and $$F$$ be on $$AB$$ and $$G$$ be outside $$ABC$$ such that $$DG \mid \mid EF$$ and $$\angle DEF = \angle GFE = 90^{\circ}$$. Let $$AC$$ intersect $$DG$$ at $$J$$ and intersect $$FG$$ at $$K$$. It is known $$CD=25$$ and $$JK=16$$. Find the length of $$EF$$.

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