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.