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.