is point A the center? if so, it forms a right angle when it intersects with the tangent at the circumference. (this is again, the famous 3-4-5 triangle, we know the answer will be 3, but how to find that for certain?)

by Pythagoras' theorem:

(BC)^2 = (AB)^2 - (AC)^2 = 5^2 - 4^2 = 25 - 16 = 9

=> BC = sqrt(9) = 3 ......as expected

if A is not the center, well, i don't know