'The center of the incircle.
The incircle is the circle which lies inside the triangle and touches
all three sides.
Returns
incenter : Point
See Also
incircle, sympy.geometry.point.Point
Examples
>>> from sympy.geometry import Point, Triangle
>>> p1, p2, p3 = Point(0, 0), Point(1, 0), Point(0, 1)
>>> t = Triangle(p1, p2, p3)
>>> t.incenter
Point2D(-sqrt(2)/2 + 1, -sqrt(2)/2 + 1)'

@property
def incenter(self):

    s = self.sides
    l = Matrix([s[i].length for i in [1, 2, 0]])
    p = sum(l)
    v = self.vertices
    x = simplify((l.dot(Matrix([vi.x for vi in v])) / p))
    y = simplify((l.dot(Matrix([vi.y for vi in v])) / p))
    return Point(x, y)
