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Erecting Trapezoids from triangle

Source: 2023 Israel TST Test 3 P3

March 23, 2023
geometrytrapezoidTSTcircumcircle

Problem Statement

Let ABCABC be a fixed triangle. Three similar (by point order) isosceles trapezoids are built on its sides: ABXY,BCZW,CAUVABXY, BCZW, CAUV, such that the sides of the triangle are bases of the respective trapezoids. The circumcircles of triangles XZU,YWVXZU, YWV meet at two points P,QP, Q. Prove that the line PQPQ passes through a fixed point independent of the choice of trapezoids.
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