def remove_middle(a, b, c):
    cross = (((a[0] - b[0]) * (c[1] - b[1])) - ((a[1] - b[1]) * (c[0] - b[0])))
    dot = (((a[0] - b[0]) * (c[0] - b[0])) + ((a[1] - b[1]) * (c[1] - b[1])))
    return ((cross < 0) or ((cross == 0) and (dot <= 0)))
def remove_middle(a, b, c):
    cross = (((a[0] - b[0]) * (c[1] - b[1])) - ((a[1] - b[1]) * (c[0] - b[0])))
    dot = (((a[0] - b[0]) * (c[0] - b[0])) + ((a[1] - b[1]) * (c[1] - b[1])))
    return ((cross < 0) or ((cross == 0) and (dot <= 0)))