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.

See complete interactive figure

Level: High School, SAT Prep, College geometry

Post your solutions or ideas in the comments.

## Thursday, July 10, 2008

### Gergonne Line

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