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 O_{1} of radius r_{1}, and the circle O_{2} of
radius r_{2} tangent to AB, BC and arc AC at C_{2}, A_{2}, and
B_{2}, respectively. Prove that r_{2} = 2r_{1}.
