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In the following diagram, is ∠CDB a central angle or an inscribed angle?

central angle

inscribed angle

The diagram shows a circle with points \( A \), \( B \), \( C \), and \( D \) on its circumference, with chords forming various angles inside the circle. To determine if \( \angle CDB \) is a central angle or an inscribed angle, we need to consider the definitions of both types of angles:

- **Central Angle**: An angle whose vertex is at the center of the circle, and whose sides are radii of the circle.
- **Inscribed Angle**: An angle whose vertex is on the circumference of the circle, and whose sides are chords of the circle.

From the diagram:

- The vertex of \( \angle CDB \) is at point \( D \), which is on the circumference of the circle.
- The sides of \( \angle CDB \) are chords \( CD \) and \( BD \).

Since the vertex is on the circumference and the sides are chords, \( \angle CDB \) is an **inscribed angle**, not a central angle.

Would you like to go into further details, or do you have any other questions?

Here are 5 related questions:
1. What is the relationship between an inscribed angle and the arc it intercepts?
2. How do central angles compare to inscribed angles that intercept the same arc?
3. Can you find the measure of \( \angle CDB \) if the intercepted arc is known?
4. What is the property of angles inscribed in a semicircle?
5. How do you calculate the arc length of a circle?

**Tip:** Inscribed angles are always half the measure of the central angle intercepting the same arc.

Explore whether ∠CDB in a circle diagram is a central angle or an inscribed angle. Learn the definitions of central and inscribed angles, and how they relate to circles and chords. Suitable for high school students studying circle geometry.

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