Arcs and Angles
A central angle equals its arc. An inscribed angle equals HALF its arc. This is the key rule for most circle angle problems.
An inscribed angle (vertex on circle) equals HALF the intercepted arc.
How It Works
What is an arc?
An arc is a piece of the circle's edge. A minor arc is the small piece (less than half). A major arc is the big piece (more than half). The whole circle = 360°.
Central angle
A central angle has its vertex (point) at the CENTER of the circle. The central angle equals the arc it cuts off. Simple: angle = arc.
Inscribed angle (THE BIG RULE)
An inscribed angle has its vertex ON the circle. It equals HALF the arc it intercepts. If the arc is 80°, the inscribed angle is 40°. This is the rule you'll use the most.
Angles in a semicircle
If an inscribed angle intercepts a semicircle (half the circle = 180° arc), the angle is 90°. Half of 180° = 90°. So any angle in a semicircle is a right angle.
Angles outside the circle
When two secants (or a secant and tangent) meet OUTSIDE the circle: angle = ½ × (big arc − small arc). Notice it's the DIFFERENCE, not the sum.