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Concyclic points

Egilea:Lamberto Lamberti
The figure shows a triangle ABC, if A, D, E, G are concyclic and B,D,E,I are concyclic, proof that C,E,I,G are concyclic. http://www.gogeometry.com/school-college/p915-triangle-circle-cyclic-quadrilateral-concyclic.htm

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