College Geometry: Outer Nagel Point, Online Education

Problem 684: Outer Nagel Point, Triangle, Excircles, Tangency points, Concurrent lines, Semi-perimeter, Ceva theorem. Level: High School, SAT, College Geometry

The figure shows a triangle ABC with the incircle I and the excircles EA and EC tangent to the sides AC, BC, and AB at the points B', C' and A', respectively. Prove that AA', B'B, and CC' concur in the outer Nagel point NB.
Christian Heinrich von Nagel (28 February 1803, Stuttgart, Germany – 27 October 1882, Ulm, Germany) was a German geometer.
 

Outer Nagel Point, Incircle, Excircles, Tsangency points
 

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