1, when the circle o and both arcs are inscribed.

R =( 1/2)R =( 1/2)* 1 = 1/2，

So: the circumference of a circle O =2∏r=2*( 1/2)*∏=∏.

2. When the circle O is inscribed with an arc and circumscribed with another arc.

There are:

X2 = [(r-r) 2]-(r 2), which means X2 = (r 2)-2rr-(1).

(x 2)+[(r-r) 2] = (r+r) 2, that is, x 2 = 4rr-(2).

Solving the equations composed of (1) and (2), we get: r=( 1/6)R= 1/6.

So: the circumference of a circle O = 2 ∏ R = 2 * (1/6) * ∏ = (1/3) ∈