In the diagram at right, $\overline{AB}$ is a diameter of $⊙L$. If $BC=5$ and $AC=12$ , use the relationships shown in the diagram to solve for the quantities listed below.  

1. $AB$  

   Hint (a):

   Start by finding the measure of $∠ACB$.

   More Help (a):

   Use the Inscribed Angle Theorem, explained in the Math Notes box in Lesson 10.1.3, to determine the measure of $∠ACB$.

   Hint 2(a):

   Since $ΔABC$ is a right triangle:
    $(AC)^2 + (BC)^2 = (AB)^2$

   Step (a):

   $\begin{array}{l} 12^2 + 5^2 = \left(AB\right)^2 \\ 169 = \left(AB\right)^2 \\ AB = 13\ \text{units} \end{array}$

2. length of the radius of $⊙L$ 

   Hint (b):

   Use the diameter, $\overline{AB}$, to find the radius.

3. $m∠ABC$  

   Hint (c):

   Use trigonometry to find the measures of the acute angles in $ΔABC$.

4. $m\overarc{ A C }$  

   Hint (d):

   $2 \cdot (m\angle ABC) = m \overarc{AC}$