Geometry + Radical Arithmetic = Headache!

Geometry Level 5

Consider a square \(ABCD\) with side of length \(4\).

Let \(E\) be a point outside \(ABCD\) such that \(\Delta CDE\) is equilateral.

Draw \(\angle CEK = 30^\circ\) such that ray \(EK \) intersects ray \(AC\) at \(G\), ray \(DC\) at \(F\), ray \(AB\) at \(P\).

If Area of \(\Delta AGP\) can be represented as:

\[a + b\sqrt{c}\] where \(c\) is independent of a perfect square.

Find \(a + b + c\).


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