prove this circles question involving polar

Question

Through a fixed point O are drawn straight lines OPQ and ORS to meet a circle in P and Q, and R and S. Prove that the locus of the point of intersection of PR and QS, as also that of the point of intersection of PR and QS, is the polar of O with respect to the circle.

Answer 1

I have converted the problem into oblique coordinates and eliminated $x_1$, $x_2$, $y_1$ and $y_2$. Then I found polar with respect to the circle and then proved both are same