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Parallelism is Sangaku configuration

Source: Kvant Magazine No. 2 2019 M2547

March 14, 2023
geometryKvant

Problem Statement

The circles ω1\omega_1 and ω2\omega_2 centered at O1O_1 and O2O_2 are externally tangent at the point TT. The circle ω3\omega_3 centered at O3O_3 is tangent to the line ABAB (the external common tangent of ω1\omega_1 and ω2\omega_2) at DD and externally tangent to ω1\omega_1 and to ω2\omega_2. The line TDTD intersects again at ω1\omega_1. Prove that O1C∥ABO_1 C \parallel AB.
[I]Proposed by V. Rastorguev[/I]
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