Online Geometry Education

Problem 535: Sawayama - Thebault's theorem. Math Education. Level: High School, SAT Prep, College Geometry

The figure shows a triangle ABC, D is the incenter of triangle ABC. Point E is taken on side AC, G and F are the centers of circles that touch BE, AC and the circumcircle of triangle ABC. Prove that G, D, and F are collinear.
 

Sawayama - Thebault's theorem
 

I have used Geometry Expressions to visualize these geometric forms and check out a variety of conjectures. Geometry Expressions is the world's first Interactive Symbolic Geometry System. This means: Geometric figures can be defined by either Symbolic Constraints or numeric locations.

You can download Geometry Expressions 2 Free Trial. It is a fully featured 30 day evaluation copy of the software. All constraints, constructions and measurements are available for you to use.
 

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