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The Medial Triangle and Concurrency at the Nagel Point


	Let ABC be a triangle and A', B', and C' be the midpoints of the sides opposite A, B, and C. Let A", B", and C" be the points of tangency of the incircles of AB'C' with B'C', BA'C' with A'C', and CA'B' with A'B'. Then A'A", B'B", and C'C" are concurrent and meet at the Nagel point.


	Contributed by: Jay Warendorff After work by: Alexander Bogomolny

The lines connecting the vertices of a triangle with the corresponding points of tangency of the three excircles are concurrent at a point called the Nagel point.

A. Bogomolny, "Nagel Point of the Medial Triangle," Interactive Mathematics Miscellany and Puzzles.

Concurrent (Wolfram MathWorld)

Medial Triangle (Wolfram MathWorld)

Nagel Point (Wolfram MathWorld)

"The Medial Triangle and Concurrency at the Nagel Point" from The Wolfram Demonstrations Project
http://demonstrations.wolfram.com/TheMedialTriangleAndConcurrencyAtTheNagelPoint/

Contributed by: Jay Warendorff

After work by: Alexander Bogomolny

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