Let \( PQ \cap AB = F \). To prove that \( OP \parallel CF \) implies that points \( C, D, F \) are collinear, we start with the angles: \[ \angle FPO = x, \quad \angle OPA = y. \] Now consider the following ratios: \[ \frac{FX}{AX} = \frac{\cos y}{\sin y} \cdot \frac{\sin x}{\cos x. \] We also have: \[ \frac{CO}{AO} = \frac{QO}{PO} \cdot \frac{\cos y}{\sin y}. \] Noticing that: \[ \frac{QO}{PO} = \frac{\sin x}{\cos x}, \] we can substitute this into our previous equation: \[ \frac{CO}{AO} = \frac{\sin x}{\cos x} \cdot \frac{\cos y}{\sin y}. \] By Thales' theorem, we conclude that: \[ OP \parallel CF. \] Thus, we have shown that \( C, D, F \) are collinear.