We are asked to determine the arc length of HJ. To do that we will use the following formula:
Given two secant lines that intercept outside a circle as follows:
We have the following relationship:
[tex]\angle x=\frac{1}{2}(\text{mCD-mAB)}[/tex]
Substituting the values we get:
[tex]29=\frac{1}{2}(96-\text{mHJ)}[/tex]
Now, we multiply both sides by 2:
[tex]58=96-mHJ[/tex]
Now, we subtract 96 from both sides:
[tex]58-96=-\text{mHJ}[/tex]
Solving the operations:
[tex]-38=-\text{mHJ}[/tex]
Now, we multiply both sides by -1:
[tex]38=\text{mHJ}[/tex]
Therefore, the measure of the arc length of HJ is 38.
