Angle of deflection from the vertex of a square

Question

I have the impression this question is somehow trivial but for some reason I'm not able to figure it out. So I'd appreciate your help.

Problem

Suppose I have a square with sides $a$, $b$, $c$, $d$. Now I shoot a ball from anywhere inside the square (except from its centre) to a corner (vertex) of the square formed by two sides, let's say $a$ and $b$ at angle $\alpha$ from $a$. What would be the angle of deflection after it hits the corner?

(In this problem I'm excluding external factors such as friction, drag and so on)

Answer 1

Consider the case when the ball doesn't hit the corner, but a point $P$ at a small distance from it. In that case the ball, after hitting two sides of the square, bounces back along a line parallel to the trajectory of the ball before hitting the sides. As $P$ approaches the corner, the distance between the two parallel lines gets smaller and smaller. In the limit, that distance vanishes and the ball, when hitting a corner, bounces back along the same path it came from.

Answer 2

Not trivial at all.

After two reflections, reflected ray remains parallel to the incident ray but have opposite sense of the velocity vector. No exception to rays emanating from points such as $P$.

After encountering a corner the ray retraces its own path. Rays go along lines that make $ (\alpha, \pi-\alpha) $ to horizontal along parallelogram edge paths as shown.