Question

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

Answer 1

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:

`58=96-mHJ`

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.