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.

Infographic Geometry problem 1143 Triangle, Circumcircle, Tangent Line, Reflection of a Point over a Line, Tangent Circles, Collinear Points