Two points $A$ and $B$ lie inside an acute angle. Construct an isosceles triangle $PQR$ whose base $PR$ lies on one side of the angle, whose third vertex $Q$ lies on the other side of the angle, and whose two lateral sides $PQ$ and $QR$ pass through $A$ and $B$, respectively.
I was thinking of reflecting $A$ and $B$ in one of the arms and then figuring out some line which will intersect the angle to give the points, but cant figure out any useful reflection. Please help. Thanks a lot.