Online Geometry

Dynamic Geometry: Exeter Point, Triangle, Median, Circumcircle, Concurrent Lines, Euler Line, GeoGebra

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.

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 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.
Static Diagram of Exeter Point

Exeter Point of a triangle

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