The point $P$ is located outside the circle with center $O$. The lines $l_1$ and $l_2$ pass through the point $P$. The line $l_1$ touches the circle in the point $A$ and the line $l_2$ intersects the circle at the points $B$ and $C$. The tangents of the circle that pass through point $B$ and $C$ intersect at the point $X$. How can I prove that $PO$ is perpendicular to $AX$?