What you’ll learn
Understand central angles.
Key idea
A central angle has its vertex at the center and sides along radii; endpoints alone are insufficient.
Vertex location distinguishes central from inscribed angles; endpoints alone are insufficient.
Worked example
Classify examples and non-examples for the concept 'Understand central angles'.
A circle has radius 4. A and B are on it and angle AOB measures 50 degrees with vertex at center O. Classify the angle and give defining evidence.
- Its vertex is at center O.
- Use that vertex location: center gives central, circumference gives inscribed.
Answer: Central angle — the vertex is the center and both sides lie along radii.
Quick Check
Classify examples and non-examples for the concept 'Understand central angles'.
A circle has radius 7. A and B are on it and angle APB measures 130 degrees with vertex at P on the circumference, distinct from A and B and from center O. Classify the angle and give defining evidence.