Online Geometry Problem 821: Adams Circle Theorem, Incenter, Incircle, Gergonne Point, Contact triangle, Parallel, Six Concyclic points, Concentric Circles. Level: High School, SAT Prep, College, Mathematics Education

Given a triangle ABC, the incenter I, the incircle, and the Gergonne point G. Construct the contact triangle A'B'C' . Adams theorem (1843) states that the parallels to the sides of the contact triangle from G, intersect the side of the triangle ABC in 6 points lying on a circle (Adams' circle) concentric to the incircle.

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