Problem 1311: Inscribed Triangle, Circle, Circumcircle, Concyclic Points, Measurement.

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The figure below shows a triangle ABC inscribed in a circle O. A line cuts the arc AB, AB, BC, and the arc BC at D, E, F, and G, respectively, so that A, E, F, and C are concyclic points. If AD = 12, DE = 8, and EG = 11, find AG.