Question 3
Let $PQRS$ be a cyclic quadrilateral such that the segments $PQ$ and $RS$ are not parallel. Consider the circles through $P,Q$ and the circles through $R,S$. Determine the set $A$ of tangency points of circles in these two sets.
Editorial convention (AI): tangent circles are understood to be distinct and to have exactly one common point. The source also discusses a different convention; both interpretations are explained in the solution.
Editorial convention (AI): tangent circles are understood to be distinct and to have exactly one common point. The source also discusses a different convention; both interpretations are explained in the solution.