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Geometry Problem 1148: The Enigmatic Connection: Exploring Right Triangles, Circles, and Tangents


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

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

Inradius and right triangle's quest,
Circles and tangents put to the test.
Unveiling the connection profound,
Prove their harmony can be found.

See the dynamic diagram of problem 1148 


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Last updated Jun 17, 2023