Geometry Problems, Online Education

Problem 1104: Right Triangle, Incircle, Circumcircle, Inscribed Circle, Radius, Tangent. Level: High School, SAT Prep, College Geometry

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In a right triangle ABC (see the figure below) with circumcircle Q, the incircle O (radius r) is tangent to AB, BC, and AC at D, E, and F, respectively. Circle O1 (radius x) is tangent to AB, BC and arc AC at H, M, N, respectively. Prove that x = 2r = a + c - b.

 

Geometry Problem 1104, Right Triangle, Incircle, Circumcircle, Inscribed Circle, Radius, Tangent


 

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Last updated: Mar 30, 2015, by Antonio Gutierrez