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Trig condition for cyclic ABCD

Source: IMO Shortlist 1997, Q23, British training sheet

February 12, 2005
trigonometrygeometrycircumcircleIMO Shortlistcyclic quadrilateral

Problem Statement

Let ABCD ABCD be a convex quadrilateral. The diagonals AC AC and BD BD intersect at K K. Show that ABCD ABCD is cyclic if and only if AK \sin A \plus{} CK \sin C \equal{} BK \sin B \plus{} DK \sin D.
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