# Geometry Problem 1143: Triangle, Circumcircle, Tangent Line, Reflection of a Point over a Line, Tangent Circles, Collinear Points. Level: High School, SAT Prep, Honors Geometry, College, Math Education

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 The infographic below shows a triangle ABC with a line L tangent to the circumcircle O at T. L intersects CB, AC, and AB (extended if necessary) at A1, B1, and C1, respectively. A2, B2, and C2, are the reflections of T over CB, AC, and AB, respectively. Lines A1A2, B1B2, and C1C2 determine the triangle A3B3C3. Prove that (1) Points A2, B2, and C2 are collinear; (2) Circle O and the circumcircle of triangle A3B3C3 are tangent at D.    See also: Art of problem 1143 using iPad Apps
 Home | Search | Geometry | Problems | All Problems | Open Problems | Visual Index | 10 Problems | 1141-1150 | Triangle | Circumcircle | Circle | Reflection | Tangent Line | Tangent Circles | Collinear Points | Email | Solution / comment.Last updated: Jul 27, 2015 by Antonio Gutierrez.