Central and Inscribed Angles

A central angle is an angle whose vertex is at the center of the circle and whose sides are radii that extend to the circumference.

An inscribed angle is an angle formed by two chords in a circle which have a common endpoint. The vertex of the angle is on the circumference of the circle.

The circumference of a circle can be calculated using the formula C = 2πr, where r is the radius of the circle.

The measure of a central angle is equal to the measure of its intercepted arc.

The measure of an inscribed angle is half the measure of its intercepted arc.

A radius is a line segment from the center of the circle to any point on its circumference.

A chord is a line segment whose endpoints lie on the circumference of the circle.

The area of a circle can be calculated using the formula A = πr², where r is the radius.

An arc is a portion of the circumference of a circle.

The measure of the arc is equal to the measure of the central angle that intercepts it.