Geometry Problem 1085: Intersecting Circles, Concyclic Points, Cyclic Quadrilateral. Level: High School, SAT Prep, College, Math Education

The figure below shows circles O and Q intersecting at A and B and a line CDEF ( C and E on circle O, D and F on circle Q). CA and BF meet at H, DA and BE meet at G. Prove that A, B, H, and G are concyclic points.
 

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