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OB_|_CD wanted, concurrent circles (2021 Kyiv City MO 9.5.1)

Source:

February 15, 2021
geometrycirclesperpendicular

Problem Statement

Two circles ω1\omega_1 and ω2\omega_2 intersect at points AA and BB. A line passing through point BB intersects ω1\omega_1 for the second time at point CC and ω2\omega_2 at point DD. The line ACAC intersects circle ω2\omega_2 for the second time at point FF, and the line ADAD intersects the circle ω1\omega_1 for the second time at point EE . Let point OO be the center of the circle circumscribed around △AEF\vartriangle AEF. Prove that OB⊥CDOB \perp CD.
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