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construct quadrilateral, given 2 circumcenters + 2 incenters, by diagonals

Source: 2015 Sharygin Geometry Olympiad Correspondence Round P16

August 2, 2018
geometrycircumcircleincenter

Problem Statement

The diagonals of a convex quadrilateral divide it into four triangles. Restore the quadrilateral by the circumcenters of two adjacent triangles and the incenters of two mutually opposite triangles