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 E_A and E_C 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 N_B.
Christian Heinrich von Nagel (28 February 1803, Stuttgart, Germany – 27 October 1882, Ulm, Germany) was a German geometer.