Online Geometry

Dynamic Geometry: Exeter Point, Triangle, Median, Circumcircle, Concurrent Lines, Euler Line, GeoGebra, HTML5 Animation for Tablets (iPad, Nexus, Samsung). Levels: School, College, Mathematics Education

Given a triangle ABC (see the dynamic figure below),  Medians AA1, BB1, and CC1, meet the circumcircle O at A2, B2, and C2, respectively. Tangents at A, B, and C form a triangle A3B3C3. Prove that (1) Lines A3A2, B3B2, and C3C2 are concurrent at a point E, called the Exeter point. (2) E lies on the Euler line. 

See also: Exeter Point Puzzle.

Reference
Kimberling, Clark. "Encyclopedia of Triangle Centers: X(22)"

Dynamic Geometry Environment (DGE) or Interactive Geometry Software (IGS) of the Exeter Point

The interactive demonstration above was created with GeoGebra.

To stop/play the animation: tap the icon in the lower left corner.
To reset the interactive figure to its initial state: tap the icon in the upper right corner.
To manipulate the interactive figure: tap and drag points or lines.
  

GeoGebra
GeoGebra is free and multi-platform dynamic mathematics software for all levels of education that joins geometry, algebra, tables, graphing, statistics and calculus application, intended for teachers and students.
 

Exeter Point of a triangle
 


 

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