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MEMO 2010, Problem T-6: Equal angles

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September 12, 2010
ratiogeometryparallelogramcircumcirclecyclic quadrilateralIMO Shortlistgeometry proposed

Problem Statement

Let AA, BB, CC, DD, EE be points such that ABCDABCD is a cyclic quadrilateral and ABDEABDE is a parallelogram. The diagonals ACAC and BDBD intersect at SS and the rays ABAB and DCDC intersect at FF. Prove that ∢AFS=∢ECD\sphericalangle{AFS}=\sphericalangle{ECD}.
(4th Middle European Mathematical Olympiad, Team Competition, Problem 6)
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