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8

Part of 1993 Moldova Team Selection Test

Problems(1)

rove that the quadrilateral $O_1O_2O_3O_4$ is a parallelogram.

Source: Moldova TST 1993

8/8/2023
Inside the parallelogram ABCDABCD points M,N,KM, N, K and LL{} are on sides AB,BC,CDAB, BC, CD{} and DADA, respectively. Let O1,O2,O3O_1, O_2, O_3 and O4O_4 be the circumcenters of triangles repesctively MBN,NCK,KDLMBN, NCK, KDL and LAMLAM{}. Prove that the quadrilateral O1O2O3O4O_1O_2O_3O_4 is a parallelogram.
geometryparallelogramcircumcircle