Math
Central and inscribed angles.
Definition
A central angle has its vertex at the center of a circle and equals its intercepted arc. An inscribed angle has its vertex on the circle and equals half its intercepted arc. This relationship is known as the Inscribed Angle Theorem.
Examples
Real-world.
- 1 A central angle of 80° intercepts an 80° arc, while an inscribed angle intercepting the same arc measures 40°
- 2 An inscribed angle that intercepts a semicircle (180° arc) is always 90° — this is Thales' theorem
Key Fact
Inscribed angle = ½ · intercepted arc; Central angle = intercepted arc