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Tangent circles in a quadrilateral

Source: ARO Regional stage 2023 9.5

February 16, 2023
geometryRussia

Problem Statement

Let ABCDABCD be a cyclic quadrilateral such that the circles with diameters ABAB and CDCD touch at SS. If M,NM, N are the midpoints of AB,CDAB, CD, prove that the perpendicular through MM to MNMN meets CSCS on the circumcircle of ABCDABCD.
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