Angles & Circles
Central Angles
A central angles is an angle formed by two radii and vertex at the center of a circle. The measure of the intercepted arc is equal to the measure of the central angle.
Inscribed Angles
An inscribed angle is an angle formed by two intersecting chords or secants with its vertex "on" the circle. The measure of the intercepted arc is equal to double the measure of the inscribed angle (or, the measure of the angle is equal to half the measure of the intercepted arc).
Tangent & Chord Angles
An angle formed by an intersecting tangent and chord has its vertex "on" the circle. The intercepted arc is equal to double the measure of the angle (or, the measure of the angle is equal to half the measure of the intercepted arc).
Intersecting Chords/Secants
An angle formed by two intersecting chords or secants has its vertex inside the circle. Two sets of vertical angles are created. The measure of an angle is equal to half the sum of the intercepted arcs (intercepted by the pair of vertical angles).
Angles Outside the Circle
An angle formed by two secants, a secant and a tangent, or two tangents, has its vertex outside the circle if the lines intersect outside the circle. The measure of the angle is equal to half the difference of the intercepted arcs (the "near" arc should be subtracted from the "far" arc).
Summation
Angles can be determined based on the location of the vertex:
- Vertex @ center: angle is equal to the intercepted arc
- Vertex on the circle: angle is equal to half of the intercepted arc
- Vertex inside the circle: angle is equal to half the sum of the intercepted arcs
- Vertex outside the circle: angle is equal to half the difference of the intercepted arcs