MathDB
fixed point, cirrcumcircles of 2 squares - Chile 2002 L2 P3

Source:

September 1, 2022
geometryFixed pointchilean NMO

Problem Statement

Given the line ABAB, let MM be a point on it. Towards the same side of the plane and with bases AMAM and MBMB, squares AMCDAMCD and MBEFMBEF are constructed. Let NN be the point (different from MM) where the circumcircles circumscribed to both squares intersect and let N1N_1 be the point where the lines BCBC and AFAF intersect. Prove that the points NN and N1N_1 coincide. Prove that as the point MM moves on the line ABAB, the line MNMN moves always passing through a fixed point.
Back to ProblemsView on AoPS