https://file.aiquickdraw.com/mathbot/file/1727605032582bhh0vedh.jpg

Let's go over the questions and fill in the blanks from the image.

1. **One degree is equal to sixty** _minutes_.
2. **The vertex of an inscribed angle lies on the** _circle_.
3. **A/An** _second_ **is equal to 1/60 of a minute**.
4. **___ concentric ___ circles have the same center but radii of different lengths**.
5. **The part of a circle included between two of its points is a/an** _arc_.
6. **An angle whose sides are chords of a circle and whose vertex lies on the circle is a/an** _inscribed angle_.
7. **A circle is** _circumscribed_ **about a polygon if the circle passes through all the vertices of a polygon**.
8. **If a/an** _right_ **angle is inscribed in a circle, then its intercepted arc is a semicircle**.
9. **A circle is** _inscribed_ **in a polygon if every side of the polygon is tangent to the circle**.

Next, let's handle the calculations for the angles:

10. **If inscribed ∠B intercepts AC, which measures 84, then m∠B =** _42°_ (since an inscribed angle is half the measure of its intercepted arc).
11. **If central ∠C measures 58 and intercepts BD, then mBD =** _58°_ (a central angle is equal to the measure of the intercepted arc).
12. **If ∠B, formed by a tangent and a chord, measures 15 and intercepts AC, then mAC =** _30°_ (the angle formed by a tangent and a chord is half the intercepted arc).
13. **Intercepted BC measures 128 and is formed by tangents AB and AC. ∠A is formed by the two tangents and measures** _64°_ (the angle between two tangents is half the difference of the intercepted arcs).

Would you like a more detailed explanation for any specific point?

Here are 5 related questions to think about:
1. What is the relationship between central and inscribed angles in a circle?
2. How do concentric circles help in real-world applications?
3. How can you calculate the length of an arc?
4. Why is a tangent to a circle perpendicular to the radius at the point of contact?
5. What is the significance of a circumscribed circle around a polygon?

**Tip:** Always remember that an inscribed angle is half of the intercepted arc, and a central angle is equal to its intercepted arc.

Fill in the blanks related to geometry and circles (as seen in the image).

This resource provides a step-by-step guide to understanding key concepts in circle geometry, including theorems on inscribed and central angles, tangent and chord relationships, and the connection between arcs and angles. Ideal for high school students in Grades 9-11.

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