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Dynamic Geometry Problem 1148: Right Triangle, Circle,  Incircle, Circumcircle, Tangent, Radius. GeoGebra, HTML5 Animation for Tablets (iPad, Nexus). 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.

Dynamic Geometry Environment (DGE) or Interactive Geometry Software (IGS) of Problem 1148

The interactive demonstration above was created with GeoGebra.

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See the static diagram of problem 1148

 

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