Inscribed Angles and Central Angles

Central angle: Vertex at the center of the circle. The central angle equals the arc it intercepts. Inscribed angle: Vertex ON the circle. An inscribed angle is half the central angle that intercepts the same arc: [formula] Special cases: - An inscribed angle that intercepts a semicircle (diameter) is always 90°. - Inscribed angles that intercept the same arc are equal.

Example: A central angle is 80°. What is the inscribed angle that intercepts the same arc?

The most tested fact: any inscribed angle subtending a diameter is exactly 90°. If you see a triangle inscribed in a circle with one side being a diameter, the angle opposite that side is a right angle.