This is very simple!!! Your 'stuckness' will disappear in a minute.
∠AOB = ∠COB = 90º
1st Find an angle AOC ∠AOC = ∠AOB + ∠COB
∠AOC = 2[arccos( AO / OB )] = 108.6293306º
2nd Find the central angle of a major arc ADC
That angle is 360º - ∠AOC = 251.3706694º
3rd Find the length of ADC
ADC = 2 * 7 * pi * ( 251.3706694 / 360 ) = 30.711