Okay now i restructured my code

Well, now you use a totally different method of computation: Before it was checking for the point on the segment that is closest to the circle's origin, now you use the implicit circle formula to check for identical points on the line. That is a replacement, not a restructuring!

The originally used method has the advantage that the distance of the intersection along the segment was computed, and that is good to judge whether the intersection is inside or outside the segment's range. The now use method does not compute that distance anywhere. So ...

a) you go back and use the original method, together with the 2 conditions I've posted above; I would suggest this way (in assumption that the original method works well for lines),

or

b) you check whether the computed intersections(s) are between the end-points of the segment. For this you can use the projection method, too.