The length of Arc AC of a circle is 1/6th of the circumference of the circle.B is the midpoint of the Arc AC.
R=2 cm
Circumference= 2*3.14*2 = 12.56
l(AC)~ 2 cm
l(AB)~ 1 cm
Since the angle between arc AC is 60 degree, the angle between arc AB is 30 degree.
Now seg AB creates a triangle with two radii of 2 cm with an angle of 30 degree between them.
the area of this triangle can be calculated by the formule
A= 0.5* side1 * side 2 * sin(angle between them)
therefore, A= 0.5* 2 * 2 * sin30
A= 1 cm
now, apply heron's formula to calculate the remaining side length.