Geometry Problem 1455: Nagel Point, Excircles, Incircle, Congruent Segments
Given a triangle ABC with the incircle I. Let EA, EB, EC
be the excircles and TA, TB, TC be the extouch points. The Lines ATA, BTB, CTC concur in the Nagel point N and cuts the
incircle at IA, IB, IC. Prove that AIA = NTA,BIB = NTB, CIC = NTC.
The Nagel point is the point of intersection of the three lines that each connect a vertex of the triangle to the point of contact of the corresponding excircle with the opposite side of the triangle. An excircle of a triangle is a circle that is tangent to one side of the triangle and to the extensions of the other two sides.
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