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Set of points

Source: 2014 Czech & Slovak Mathematical Olympiad, Rnd. III, Cat. A

May 20, 2014
projective geometrygeometry unsolvedgeometryLocuslocus of points

Problem Statement

A segment ABAB is given in (Euclidean) plane. Consider all triangles XYZXYZ such, that XX is an inner point of ABAB, triangles XBYXBY and XZAXZA are similar (in this order of vertices), and points A,B,Y,ZA, B, Y, Z lie on a circle in this order. Find the locus of midpoints of all such segments YZYZ.
(Day 1, 2nd problem authors: Michal Rolínek, Jaroslav Švrček)
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