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Circles and parallelogram

Source: Kyiv City MO 2021 Round 1, Problem 10.3

December 21, 2023
geometryparallelogram

Problem Statement

Circles ω1\omega_1 and ω2\omega_2 with centers at points O1O_1 and O2O_2 intersect at points AA and BB. Let point CC be such that AO2CO1AO_2CO_1 is a parallelogram. An arbitrary line is drawn through point AA, which intersects the circles ω1\omega_1 and ω2\omega_2 at points XX and YY, respectively. Prove that CX=CYCX = CY.
Proposed by Oleksii Masalitin
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