Inscribed Angle Theorem

Inscribed Angle Theorem

The inscribed angle theorem states that an inscribed angle in a circle is equal to one-half the central angle. An alternative way of stating the theorem is that the central angle is twice the inscribed angle.

Terminology

Inscribed Angle Notation
Variable Description
The inscribed angle is the angle from a point along the perimeter of the circle to the inscribed arc.
The central angle is the angle measurement at the center of the circle to the inscribed arc.
The inscribed arc is the distance traveled along the perimeter of the circle formed by the inscribed angle.

Cases

Inscribed Angle Theorem Case 1 Inscribed Angle Theorem Case 2 Inscribed Angle Theorem Case 3

Usage

Inscribed Angle Notation