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# Geometry Problem 1297

### Elements: Arbelos, Semicircles, Diameters, Circle, Incircle, Tangent, Angle Bisector

The figure below shows an arbelos ABC (AB, BC, and AC are semicircles of centers O_{1}, O_{2}, and O).
The incircle of the arbelos is tangent to semicircles AC, AB, and BC at T,
T_{1}, and T_{2}, respectively. Prove that TB is the bisector of the
angle ATC.

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