KöMaL 2022 B5241

In a triangle $ABC$, the centre of the circumscribed circle is $O$, and $\angle ABC > 90^\circ$. The tangent drawn to the circumscribed circle at $C$ intersects line $AB$ at point $P$, and the perpendicular drawn from $P$ to $BC$ intersects line $OC$ at $Q$. Prove that $AB$ is perpendicular to $AQ$.