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Circumcircles in a parallelogram

Source: Bundeswettbewerb Mathematik 2024, Round 1 - Problem 3

March 8, 2024
geometrycircumcirclegeometry proposedAngle Chasingparallelogram

Problem Statement

Let ABCDABCD be a parallelogram whose diagonals intersect in MM. Suppose that the circumcircle of ABMABM intersects the segment ADAD in a point E≠AE \ne A and that the circumcircle of EMDEMD intersects the segment BEBE in a point F≠EF \ne E. Show that ∠ACB=∠DCF\angle ACB=\angle DCF.
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