Geometry of Arcs and Angles Investigation
Central Angles
A central angles is an angle formed by two radii and vertex at the center of a circle.
What do you notice about the measure of the central angle and the angle of the intercepted arc, shown as below?
Inscribed Angles
An inscribed angle is an angle formed by two intersecting chords or secants with its vertex "on" the circle.
What do you notice about the measure of the inscribed angle, , and the angle of the intercepted arc below?
Tangent & Chord Angles
An angle formed by an intersecting tangent and chord has its vertex "on" the circle.
What do you notice about the measure of this special inscribed angle, , and the angle of the intercepted arc, shown below?
Exterior Angles
Exterior angles are 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.
What do you notice about the measure of the exterior angle, , and the angle of the two intercepted arcs (minor arc) and (major arc) shown below?