Given a triangle ABC with the incircle I. Let E_{A}, E_{B}, E_{C}
be the excircles and T_{A}, T_{B}, T_{C} be the extouch points. The Lines AT_{A}, BT_{B}, CT_{C} concur in the Nagel point N and cuts the
incircle at I_{A}, I_{B}, I_{C}. Prove that AI_{A} = NT_{A},BI_{B} = NT_{B}, CI_{C} = NT_{C}.

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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