MathDB
Four points are concyclic

Source: Moldova IMO-BMO TST 2003, day 1, problem 3

August 14, 2008
geometrycircumcirclepower of a pointradical axis

Problem Statement

Let ABCD ABCD be a quadrilateral inscribed in a circle of center O O. Let M and N be the midpoints of diagonals AC AC and BD BD, respectively and let P P be the intersection point of the diagonals AC AC and BD BD of the given quadrilateral .It is known that the points O,M,Np O,M,Np are distinct. Prove that the points O,N,A,C O,N,A,C are concyclic if and only if the points O,M,B,D O,M,B,D are concyclic. Proposer: Dorian Croitoru
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