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.