Problem 683: 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 excircles E_A, E_B, E_C tangent to the sides at the points A', B' and C'. Prove that AA', BB', and CC' concur in the Nagel point N.
Christian Heinrich von Nagel (28 February 1803, Stuttgart, Germany – 27 October 1882, Ulm, Germany) was a German geometer.