import math


def y_coord_on_circle(xcoord, xcen, ycen, radius):
    """
    
    Return the Y coordinates of the intersection point between the
    vertical line at xcoord and the circle at centre (xcen, ycen)
    and given radius.
    
    """
    xdiff = xcoord - xcen
    # The problem is not solveable if the line is outside the circle.
    if xdiff < -radius or xdiff > radius:
        return None
    
    rsqxsq = (radius * radius) - (xdiff * xdiff)
    ydiff = math.sqrt(rsqxsq)
    return (ycen-ydiff, ycen+ydiff)