BG-MO 1981 Problem 6

Planes $\alpha,\beta,\gamma,\delta$ are tangent to the circumsphere of a tetrahedron $ABCD$ at points $A,B,C,D$ , respectively. Line $p$ is the intersection of $\alpha$ and $\beta$ , and line $q$ is the intersection of $\gamma$ and $\delta$ . Prove that if lines $p$ and $CD$ meet, then lines $q$ and $AB$ lie on a plane.