Lines AB and BC are intersecting tangents from the same circle and are thus equal.
AB = BC
3x + 12 = 7x - 8 || Adding 8 while subtracting 3x from both sides gives:
7x - 3x = 12 + 8
4x = 20 || Dividing both sides by 4 gives
[tex]\begin{gathered} \frac{4x}{4}=\frac{20}{4} \\ x=5 \end{gathered}[/tex]Therefore, x = 5
AB = 3x + 12 || where x = 5
AB = 3(5) + 12
AB = 15 + 12 = 27
AB = 27
