Join AC
AC = 17 (diameter of the big circle)
Let angle OAC = x,
AC = o, OA = c, OC = a
In triangle OCA by using cosine law we get:
cos(x) = (o^2 + c^2 - a^2)/(2*c*o)
=> cos(x) = (17^2 + 12^2 - 12^2)/(2*12*17)
=>cos(x) = 17/24
=> x = 44.900527961
Now angle BOC = 2*x ( because of triangle exterior angle theorem)
Therefore angle BOC = 89.801055922
Now let BC = m, OB=n and OC = b and angle BOC = y
Using cosine law in triangle BOC we get
m^2 = n^2 + b^2 - 2*n*b*cos(y)
=> m^2 = 5^2 + 12^2 - 2*5*12*cos(y)
=> m^2 = 25 + 144 - 120*0.0034722222
=> m = 12.9839644691
Therefore BC = 12.984 units