From the line equation, we can deduce
This implies that any point on the line can be written as
So, given any two points
their distance will be
So, we can compute the distance between two points on the line just by knowing their y coordinates!
Now, the equation of a circle with center and radius 5 is
which we can reform as
The points of intersection between the circle and the line are given by the system between the two equations:
From the second equation we can deduce . Plugging this value in the first equation yields
Solving this equation for yields
Now we have the two values
Which implies that the distance length of AB is