69-New or old? Three lines concurrents

Let $ABC$ be a triangle, let three points $A_0,B_0,C_0$ lie on $BC,CA,AB$ such that $A_0,B_0,C_0$ are collinear. Let circle $(P)$ which center $P$ lie on the line $\overline{A_0B_0C_0}$. Denote $A_1,B_1,C_1$ are reflection of $A_0,B_0,C_0$ in $(P)$ show that $AA_1,BB_1,CC_1$ are concurrent.