MathDB

23

Part of 1997 IMO Shortlist

Problems(1)

Trig condition for cyclic ABCD

Source: IMO Shortlist 1997, Q23, British training sheet

2/12/2005
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.
trigonometrygeometrycircumcircleIMO Shortlistcyclic quadrilateral