Consider the sub-triangle formed by the three points where the circle touches the large triangle. This is also an equilateral traingle because each angle is 60 degrees. Once you realize that is it just basic trigonomtry to get the rest as shown in this diagram.
Orange = 6a+2b = (3*31/2+2*pi)/6 =~ 1.91322
Green = 4b = (4*pi - 3*31/2)/6 =~ 1.22836
Michael Shackleford, A.S.A.