The intersection between a trajectory and the circles in the same area
Let a be a number somewhere between the radius and diameter of the larger circles (if they have different radii). 
Generate a grid of square tiles of side length a, so that grid(i,k) is the square from (i*a,k*a) to ((i+1)*a, (k+1)*a).
Each tile of the grid contains a list with pointers to circles or indices into the circle array.
For each circle, register it with each tile that it intersects with. Should be less than 4.

Now to test the point (x,y) of the trajectory for circle intersections resp. containment inside the corresponding disk, you only need to test it against the list of circles in tile ((int)(x/a), (int)(y/a).
I am new in coding. Now I have a question. I have an object who keep moving in an rectangle area. And I also have a lot of circle in this area too. I want to get all the intersection point between the trajectory and the all the circle. As the object is moving step by step, so was thinking that I can calculate the distance between the position of object and all the centre of each circle and compare the distance with radius of the circle. But I think that this will do a lot of computation as you need to calculate the distance at each step. Do you have any good idea or reference. By the way, I am woking on python. Thank you. As I do not have enough reputation , I can not add a picture about the problem