MathDB
Collinearity!

Source: Romania TST Day 5 Problem 1

January 21, 2015
geometrycircumcircleprojective geometrytrigonometry

Problem Statement

Let ABCABC a triangle and OO his circumcentre.The lines OAOA and BCBC intersect each other at MM ; the points NN and PP are defined in an analogous way.The tangent line in AA at the circumcircle of triangle ABCABC intersect NPNP in the point XX ; the points YY and ZZ are defined in an analogous way.Prove that the points XX , YY and ZZ are collinear.
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