Given a triangle ABC (see the dynamic figure
below), Medians AA_{1}, BB_{1}, and CC_{1}, meet the circumcircle O at A_{2}, B_{2}, and C_{2}, respectively. Tangents at A, B, and C form a triangle A_{3}B_{3}C_{3}. Prove that (1) Lines A_{3}A_{2}, B_{3}B_{2}, and C_{3}C_{2}
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
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Static Diagram of Exeter Point
