'The angle bisectors of the triangle.
An angle bisector of a triangle is a straight line through a vertex
which cuts the corresponding angle in half.
Returns
bisectors : dict
Each key is a vertex (Point) and each value is the corresponding
bisector (Segment).
See Also
sympy.geometry.point.Point, sympy.geometry.line.Segment
Examples
>>> from sympy.geometry import Point, Triangle, Segment
>>> p1, p2, p3 = Point(0, 0), Point(1, 0), Point(0, 1)
>>> t = Triangle(p1, p2, p3)
>>> from sympy import sqrt
>>> t.bisectors()[p2] == Segment(Point(0, sqrt(2) - 1), Point(1, 0))
True'

def bisectors(self):

    s = self.sides
    v = self.vertices
    c = self.incenter
    l1 = Segment(v[0], Line(v[0], c).intersection(s[1])[0])
    l2 = Segment(v[1], Line(v[1], c).intersection(s[2])[0])
    l3 = Segment(v[2], Line(v[2], c).intersection(s[0])[0])
    return {v[0]: l1, v[1]: l2, v[2]: l3}
