Draw the figure. points B and C must both be on the circle. Now connect both points B and C to the circle center O.
Since both AB and AC are tangent to the circle then AB = AC
Now draw the line AO
<OAB and <OAC are equal.
Since BAC = 120
<OAB = 60 and <OBA = 90 deg and therefore <AOB is 30 deg.
So sin<AOB = sin 30 = 1/2 = AB/ OA and
OA = 2 AB
figure and proof is also given in below attached pic