Since the line BC is tangent to the circle we know that the angle CBA is a right angle, hence the triangle is a right one and we can apply the pythagorean theorem.
Now, we know that:
[tex]AB=5[/tex]since the radius is 5. Furthermore we also know that:
[tex]\begin{gathered} AD+DC=AC \\ 5+7.4=AC \\ AC=12.4 \end{gathered}[/tex]Now, in thie case the pythagoean therorem is:
[tex]AB^2+BC^2=AC^2[/tex]Plugging the values we know and solving for BC we have:
[tex]\begin{gathered} 5^2+BC^2=12.4^2 \\ BC^2=12.4^2-5^2 \\ BC=\sqrt[]{12.4^2-5^2} \\ BC=11.35 \end{gathered}[/tex]Therefore BC is 11.35.
