Gergonne Line

Proposition
Given a triangle ABC, D, E, and F are the points of contact of the incircle with the sides, as shown. AC and DF meets at B', BC and EF meets at A', and AB and DE meets at C'. Prove that A', B', and C' are collinear.

The line A'B'C' is called Gergonne Line and the points A',B'C' are called Nobbs' points.



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Level: High School, SAT Prep, College geometry

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Geometry Problem 86

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Intouch and Extouch Triangles, Area. Level: High School, SAT Prep, College geometry

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