Line segment  AB

1. Arcs are drawn on both the side of line segment AB 
from the vertices A and B
2. The intersecting points of the arcs are C and D.
3. After joining the intersecting points, we will get line segment CD
 which divides AB into two equal parts.

Intersecting point of line segment and segement bisector is E, 
where AE=BE

Segment

Segment bisector

Midpoint of segment

Author- Shriranjani, IT for Change, Bengaluru
License- CC BY SA 4.0

Line = 8 (slider from 3 to 8, step 1)
A = (-1.2, 0.86)
B = Point(Circle[A, Line])
f = Segment(A, B)
d = Circle(B, Line - 1)
e = Circle(A, Line - 1)
C = Intersect(d, e, 2)
D = Intersect(d, e, 1)
g = Segment(C, D)
E = Intersect(f, g)
h = Segment(A, E)
i = Segment(E, B)
F = Point(e)
G = Point(e)
c = CircleArc(A, F, G)
H = Point(d)
I = Point(d)
k = CircleArc(B, H, I)
J = Point(k)
K = Point(k)
p = CircleArc(B, J, K)
L = Point(c)
M = Point(c)
q = CircleArc(A, L, M)
r = CircleArc(B, I, H)
s = CircleArc(A, G, F)
N = (2.94, -1.28)
t = CircleArc(A, M, N)
a = true
b = true
j = true
Curve(x) = NaN