Circle: Angles

A central angle of a circle is an angle whose vertex is located at the center of the circle

Example: ∠AOB

An inscribed angle is an angle whose vertex is on a circle and whose sides each intersect the circle at another point

Example: ∠ACB

The measure of the central angle is double the measure of the inscribed angle intercepting the same arc

m∠AOB = 2 × m∠ACB

Two or more inscribed angles intercepting the same arc are equal

m∠ACB = m∠ADB = m∠AEB 

Any inscribed angle whose endpoints are a diameter is a right angle, or 90°

m∠ACB = 90°