The intersection between a trajectory and the circles in the same area
In general I would recommend to first make your algorithm work and then make it faster if you need to. You would be amazed by how fast Python in combination with a set of carefully selected libraries can be.
So for your problem, I would do the following:
1.) Install a set of libraries that makes your life easier:
   - Matplotlib for 2D plotting of the rectangle, the circle and 
     the trajectory
2.) Numpy for general purpose array manipulation
3.) Optionally Scipy for its KDTree support (nearest neighbor search)
4.) Start implementing your problem
  a.) Create a rectangle and visualize it using Matplotlib
b.) Create a set of circles and plot them within the rectangular area of 4a
c.) Create a trajectory and plot them within the rectangular area
Now the more difficult part starts. The way forward depends a little on how your trajectory is defined. For example, if your trajectory consists of line segments, you could calculate the intersection point between a circle and a line segment analytically. Three possible solutions exist, no intersection, 1 intersection (line touches circle) and 2 intersections. If your trajectory is more complex, you could discretize it by generating many points along it and than calculate if this point is on the edge of one of the circles. You have to be a little clever though about how the 3 possible solutions can be identified, because the points along the trajectory are finite. 
Another option would be to also discretize the points on the edges of the circles. This would mean that the problem reduces for a large part to nearest neighbor search for which you can use the Scipy KDTree class.
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