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XY \perp AD Assara

Source: Assara 2024 S6

October 14, 2024
geometry

Problem Statement

The points A,B,C,DA, B, C, D are marked on the straight line in this order. Circle ω1\omega_1 passes through points AA and CC, and the circle ω2\omega_2 passes through points BB and DD. On the circle ω2\omega_2, the point EE is marked so that AB=BEAB = BE, and on the circle ω1\omega_1, the point FF is marked so that CD=CFCD = CF. The line AEAE intersects the circle ω2\omega_2 a second time at point XX, and the line DFDF intersects the circle ω1\omega_1 at point YY. Prove that the XYXY lines and ADAD is perpendicular. A.D.Tereshin
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