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angle chasing in a cyclic quadrilateral, diagonals and ratio of lengths related

Source: 1996 Estonia National Olympiad Final Round grade 9

March 11, 2020
geometrycyclic quadrilateralratiodiagonalsangles

Problem Statement

The vertices of the quadrilateral ABCDABCD lie on a single circle. The diagonals of this rectangle divide the angles of the rectangle at vertices AA and BB and divides the angles at vertices CC and DD in a 1:21: 2 ratio. Find angles of the quadrilateral ABCDABCD.