MathDB
Vmo 2006 a2

Source:

February 28, 2006
geometrycircumcirclemodular arithmeticgeometry unsolved

Problem Statement

Let ABCDABCD be a convex quadrilateral. Take an arbitrary point MM on the line ABAB, and let NN be the point of intersection of the circumcircles of triangles MACMAC and MBCMBC (different from MM). Prove that: a) The point NN lies on a fixed circle; b) The line MNMN passes though a fixed point.