https://file.aiquickdraw.com/mathbot/file/1727055574557pns4ukhr.jpg

The image contains a circle with points \(A\), \(B\), and \(C\) marked on its circumference, while point \(O\) is the center of the circle. There are two angles labeled: 

- **Sudut pusat**: This is the angle at the center of the circle, labeled as \(\angle AOB\), formed by the lines \(OA\) and \(OB\), which are radii of the circle.
- **Sudut keliling**: This is the angle on the circumference of the circle, labeled as \(\angle ACB\), formed by the points \(A\), \(C\), and \(B\).

The relationship between the central angle \(\angle AOB\) and the inscribed angle \(\angle ACB\) that subtend the same arc (arc \(AB\)) follows the **Inscribed Angle Theorem**, which states that:

\[
\angle ACB = \frac{1}{2} \times \angle AOB
\]

Would you like further explanation on this theorem or how to apply it? 

Here are 5 related questions to extend this information:
1. What happens to the inscribed angle if the central angle is doubled?
2. Can the inscribed angle ever be equal to the central angle? Why or why not?
3. How does this theorem apply if point \(C\) is moved to different positions on the circle?
4. What is the measure of an inscribed angle subtending a semicircle?
5. What other properties of circles are important in solving problems involving angles?

**Tip**: Always remember that an inscribed angle that subtends a semicircle (half of the circle) will always be a right angle (90 degrees).

Determine the relationship between the central angle ∠AOB and the inscribed angle ∠ACB in a circle where A, B, and C are points on the circumference, and O is the center.

This problem involves determining the relationship between the central angle ∠AOB and the inscribed angle ∠ACB in a circle, using the Inscribed Angle Theorem. The solution explains the key geometric concepts and provides the formula to solve the problem. Suitable for students in Grades 9-10.

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