MathDB

10

Part of 2010 Middle European Mathematical Olympiad

Problems(1)

MEMO 2010, Problem T-6: Equal angles

Source:

9/12/2010
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)
ratiogeometryparallelogramcircumcirclecyclic quadrilateralIMO Shortlistgeometry proposed