Cyclic quad
Source: Emeritus
May 24, 2005
geometrytrapezoidcircumcircleparallelogramcyclic quadrilateral
Problem Statement
The diagonals AC and BD of a cyclic ABCD intersect at E. Let O be circumcentre of ABCD. If midpoints of AB, CD, OE are collinear prove that AD=BC.
Bomb
[Moderator edit: The problem is wrong. See also http://www.mathlinks.ro/Forum/viewtopic.php?t=53090 .]