IMO 1959–1966 - Longlisted Problems (individual years unknown) Question 15

(POL) Points $A,B,C,D$ lie on a circle such that $AB$ is a diameter and $CD$ is not. If the tangents at $C$ and $D$ meet at $P$ while $AC$ and $BD$ meet at $Q$, show that $PQ$ is perpendicular to $AB$.