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#, 2 midpoints, 2 circumenters - All-Russian MO 2004 Regional (R4) 8.6

Source:

September 27, 2024
geometryparallelogram

Problem Statement

Let ABCDABCD be a quadrilateral with parallel sides ADAD and BCBC, MM and NN are the midpoints of its sides ABAB and CDCD, respectively. The straight line MNMN bisects the segment connecting the centers of the circumcircles of triangles ABCABC and ADCADC. Prove that ABCDABCD is a parallelogram.
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