def intersect_quarter_circle_with_line(x=0,y=0,r=1):
    """
    evaluates the intersection point of:
    - the bottom left quater of circle whose center is in (r,r) with radius r
    - the line going through (x,y) with a slope of 1
    """
    xc = r + x/2 - y/2 - (2*r**2 - x**2 + 2*x*y - y**2)**0.5 / 2
    yc = xc  + (y - x)
    return (xc, yc)