# Geometry


class Solution:
    def checkOverlap(
        self,
        radius: int,
        x_center: int,
        y_center: int,
        x1: int,
        y1: int,
        x2: int,
        y2: int,
    ) -> bool:
        if x1 <= x_center <= x2 and y1 <= y_center <= y2:
            return True

        def notOverlaps(start1, end1, start2, end2):
            return end1 < start2 or end2 < start1

        def overlaps(start1, end1, start2, end2):
            return not notOverlaps(start1, end1, start2, end2)

        def shift(interval, delta):
            if interval is None:
                return None
            (start, end) = interval
            return (start + delta, end + delta)

        def circleLine(r, d):
            if d < 0 or r < d:
                return None
            w = (r ** 2 - d ** 2) ** 0.5
            return [-w, w]

        segments = [
            (x1, x2),
            (x1, x2),
            (y1, y2),
            (y1, y2),
        ]
        circleSegments = [
            shift(circleLine(radius, y1 - y_center), x_center),
            shift(circleLine(radius, y_center - y2), x_center),
            shift(circleLine(radius, x1 - x_center), y_center),
            shift(circleLine(radius, x_center - x2), y_center),
        ]
        for int1, int2 in zip(segments, circleSegments):
            if int2 is None:
                continue
            (start1, end1) = int1
            (start2, end2) = int2
            if overlaps(start1, end1, start2, end2):
                return True
        return False