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Two congruent circles and parallel lines

Source: IGO 2022 Intermediate P2

December 13, 2022
geometryhomothety

Problem Statement

Two circles ω1\omega_1 and ω2\omega_2 with equal radius intersect at two points EE and XX. Arbitrary points C,DC, D lie on ω1,ω2\omega_1, \omega_2. Parallel lines to XC,XDXC, XD from EE intersect ω2,ω1\omega_2, \omega_1 at A,BA, B, respectively. Suppose that CDCD intersect ω1,ω2\omega_1, \omega_2 again at P,QP, Q, respectively. Prove that ABPQABPQ is cyclic.
Proposed by Ali Zamani
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