Detecting Rectangle collision with a Circle

Question

I have a Circle with a center point (Center_X, Center_Y) and I am detecting if a rectangle falls into it's Radius (Radius). How would I be able to perform this task? I have tried using

if (X - Center_X)^2 + (Y - Center_Y)^2 < Radius^2:
        print(1)

Then I try to draw a circle to fit over this area:

Circle = pygame.draw.circle(Window, Blue, (Center_X, Center_Y), Radius, 0)

But it doesn't seem to line up. Is there something I am doing wrong?

Answer 1

Here's what I was describing in my comments, plus changes to correct handling of the case of a circle inside a larger rectangle which Michael Anderson pointed out in a comment:

import math

def collision(rleft, rtop, width, height,   # rectangle definition
              center_x, center_y, radius):  # circle definition
    """ Detect collision between a rectangle and circle. """

    # complete boundbox of the rectangle
    rright, rbottom = rleft + width/2, rtop + height/2

    # bounding box of the circle
    cleft, ctop     = center_x-radius, center_y-radius
    cright, cbottom = center_x+radius, center_y+radius

    # trivial reject if bounding boxes do not intersect
    if rright < cleft or rleft > cright or rbottom < ctop or rtop > cbottom:
        return False  # no collision possible

    # check whether any point of rectangle is inside circle's radius
    for x in (rleft, rleft+width):
        for y in (rtop, rtop+height):
            # compare distance between circle's center point and each point of
            # the rectangle with the circle's radius
            if math.hypot(x-center_x, y-center_y) <= radius:
                return True  # collision detected

    # check if center of circle is inside rectangle
    if rleft <= center_x <= rright and rtop <= center_y <= rbottom:
        return True  # overlaid

    return False  # no collision detected