Geometry Problem 1148: The Enigmatic Connection:
Exploring Right Triangles, Circles, and Tangents
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Given a right triangle ABC with the circumcircle O, the incircle O_{1}
(with a radius of r_{1}) and the circle O_{2}
(with a radius of r_{2}), which is tangent to AB, BC, and arc AC at points C_{2}, A_{2}, and B_{2}, respectively,
the objective is to prove that r_{2} = 2r_{1}.
