Question 106
A circle $\Gamma$ and a line $\ell$, which does not intersect the circle, are given in the plane. Determine the intersection of all circles with diameters $AB$, where $\{A, B\}$ is any pair of points on the line $\ell$ for which points $P, Q, R, S$ on the circle $\Gamma$ satisfying $PQ \cap RS = \{A\}$ and $PS \cap QR = \{B\}$ exist.