Here's some hints.

For 8.28: drawing a good diagram can help. Remember that the circle is inscribed, so it is inside the rectangle and we know it is tangent to the 'top' and 'bottom' (BC and AD) and one side (AB). This creates a lot of chords and tangents to think about. One solution uses Power of a Point, but there are other fairly straightforward ones as well. It may be good to review Example 8.8 from the book too, as it has the same type of setup.

For 8.30: Here's a picture that is not very accurate to the number in the problem, but hopefully helps explains what the diagram should look like:

Note, this is a good chance to practice making the drawings yourself as well. With this as a sample, try to read through the problem one piece at a time to make sure you understand where all the points and added lines are coming from.

Hope these help get you started!