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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
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Static Diagram of Exeter Point
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