You can find by extending O to AB, thereby bisecting it. Now, recall that a circle's tangent forms a right angle with its radius at their point of intersection - i.e. . You can then find .
Now extend a horizontal line from the middle of AB (call this point S) to point T (again bisecting AB to form AS and SB). Now we have a right triangle, . You can then use trigonometry to find TA since: