from math import sqrt


def almostEqual(x, y):
    return abs(x - y) < 10**-9


def distance(a: tuple[float, float], b: tuple[float, float]) -> float:
    """Calculate the distance between two points using the Euclidean distance formula."""
    return sqrt((b[0] - a[0]) ** 2 + (b[1] - a[1]) ** 2)


def triangleArea(a: float, b: float, c: float) -> float:
    """Use herons formula: `sp = (a+b+c)/2` & `sqrt(sp(sp-a)(sp-b)(sp-c))` to calculate the area of a triangle using it's side lengths."""
    semiperimeter = 0.5 * (a + b + c)
    return sqrt(
        semiperimeter * (semiperimeter - a) * (semiperimeter - b) * (semiperimeter - c)
    )


def intersect(m1: float, b1: float, m2: float, b2: float) -> tuple[float, float]:
    """Calculate the intersection point of two lines."""
    x = (b2 - b1) / (m1 - m2)
    y = m1 * x + b1
    return x, y


def areaWithinThreeLines(
    m1: float, b1: float, m2: float, b2: float, m3: float, b3: float
) -> float | None:
    """Calculate the area of a triangle formed by three lines."""
    if m1 == m2 or m2 == m3 or m3 == m1:
        return None
    a = intersect(m1, b1, m2, b2)
    b = intersect(m2, b2, m3, b3)
    c = intersect(m3, b3, m1, b1)
    return triangleArea(distance(a, b), distance(b, c), distance(c, a))


print("Testing areaWithinThreeLines()...", end="")
assert almostEqual(areaWithinThreeLines(0, 7, 1, 0, -1, 2), 36)
assert almostEqual(areaWithinThreeLines(1, -5, 0, -2, 2, 2), 25)
assert almostEqual(areaWithinThreeLines(0, -9.75, -6, 2.25, 1, -4.75), 21)
assert almostEqual(areaWithinThreeLines(1, -5, 0, -2, 2, 25), 272.25)
assert almostEqual(areaWithinThreeLines(1, 2, 3, 4, 5, 6), 0)

# The first two lines are parallel:
assert areaWithinThreeLines(1, 2, 1, 4, 0, 7) == None

# Here, the second and third lines are parallel
assert areaWithinThreeLines(5, 2, 1, 4, 1, 6) == None
print("Passed!")