In the triangle $ABC$, the angle bisector $AK$ is drawn. The center of the circle inscribed in the triangle $AKC$ coincides with the center of the circle, circumscribed around the triangle $ABC$. Determine the angles of triangle $ABC$.
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Tags: geometry, circumcircle
In the triangle $ABC$, the angle bisector $AK$ is drawn. The center of the circle inscribed in the triangle $AKC$ coincides with the center of the circle, circumscribed around the triangle $ABC$. Determine the angles of triangle $ABC$.