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10th EMC - Angle Trisection

Source: 10th European Mathematical Cup - Problem J2

December 22, 2021
emcEuropean Mathematical Cuptrisectorgeometrycircumcircle

Problem Statement

Let ABCABC be an acute-angled triangle such that ∣AB∣<∣AC∣|AB|<|AC|. Let XX and YY be points on the minor arc BC{BC} of the circumcircle of ABCABC such that ∣BX∣=∣XY∣=∣YC∣|BX|=|XY|=|YC|. Suppose that there exists a point NN on the segment AY‾\overline{AY} such that ∣AB∣=∣AN∣=∣NC∣|AB|=|AN|=|NC|. Prove that the line NCNC passes through the midpoint of the segment AX‾\overline{AX}. \\ \\ (Ivan Novak)
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