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Equal lengths and a parallelogram

Source: Sharygin Geometry Olympiad, Final Round 2016, Problem 1 grade 9

August 4, 2016
geometryAngle Chasingparallelogramcircumcircle

Problem Statement

The diagonals of a parallelogram ABCDABCD meet at point OO. The tangent to the circumcircle of triangle BOCBOC at OO meets ray CBCB at point FF. The circumcircle of triangle FODFOD meets BCBC for the second time at point GG. Prove that AG=ABAG=AB.
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