The bisectors of angles $A$ and $C$ of triangle $ABC$ intersect the circumcircle of this triangle at points $A_0$ and $C_0$, respectively. A straight line passing through the center of the inscribed circle of a triangle $ABC$ is parallel to side $AC$ and intersects line $A_0C_0$ at point $P$. Prove that line $PB$ is tangent to the circumcircle of the triangle $ABC$.