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Static Diagram Geometry Problem 1148: Right Triangle, Circle, Incircle, Circumcircle, Tangent, Radius. Levels: School, College, Mathematics Education. Levels: School, College, Mathematics Education

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Given a right triangle ABC (see the figure above) with the circumcircle O, incircle O1 of radius r1, and the circle O2 of radius r2 tangent to AB, BC and arc AC at C2, A2, and B2, respectively. Prove that r2 = 2r1.


Right Triangle, Circle, Incircle, Circumcircle, Tangent, Radius
 


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