# 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 \(EF\).