Angles at the centre and at the rim

You will write a function that measures an angle from coordinates. You will use it to test the theorem about the centre and the rim. Then you will find which points see a diameter at a right angle.

The idea. The angle at the centre is double the angle at any point on the remaining part of the circle. The angle in a semicircle is $90^\circ$. A point inside or outside the circle does not give $90^\circ$.

Your tasks.

1. In angle_at, return the angle $pvq$ in degrees, rounded to $4$ decimals.
2. In is_double, return True when the angle $AOB$ at the centre $O = (0, 0)$ is double the angle $APB$, within $0.001$ degrees.
3. Set on_circle to the names in points that see the diameter from $(-1, 0)$ to $(1, 0)$ at a right angle.