Problem

Source: Stars of Mathematics 2012, Seniors, Problem 2

Tags: geometry, geometric transformation



Let $\ell$ be a line in the plane, and a point $A \not \in \ell$. Also let $\alpha \in (0, \pi/2)$ be fixed. Determine the locus of the points $Q$ in the plane, for which there exists a point $P\in \ell$ such that $AQ=PQ$ and $\angle PAQ = \alpha$. (Dan Schwarz)