Find the indicated measure. Assume that all segments that appear to be tangent are tangent.

Question

asked Dec 7, 2023 214k views

1 Answer

Jmyster · Answer 1 · 2023-12-12T19:10:01+0000

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:

$\angle x=(1)/(2)(\text{mCD-mAB)}$

Substituting the values we get:

$29=(1)/(2)(96-\text{mHJ)}$

Now, we multiply both sides by 2:

Now, we subtract 96 from both sides:

$58-96=-\text{mHJ}$

Solving the operations:

$-38=-\text{mHJ}$

Now, we multiply both sides by -1:

$38=\text{mHJ}$

Therefore, the measure of the arc length of HJ is 38.