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Let A' be an arbitrary point on the side BC of a triangle ABC. Denote by\alpha ,\beta ,the circles simultanously tangent to AA', A'B ,\Gamma and AA', A'C ,\Gamma, respectively, where\Gamma is the circumcircle of ABC. Prove that ,\alpha ,\beta are congruent if and only if AA' passes through the Nagel point of triangle ABC.