Geometry Problem 1181: Cyclic Quadrilateral and Tangential Quadrilateral, Diameter as a Diagonal, Incenter, Circumcenter. Problem solving

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The figure shows a cyclic quadrilateral ABCD with circumcenter O and a tangential quadrilateral BCEF with incenter O₁ (F on AB) so that O and O₁ are on BD. If CE = 10 and EF =7, find AF.

  

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