A central angle is an angle whose vertex is on the circle. An inscribed angle is an angle whose vertex is on the circle and whose sides contain chords of the circle.
An arc is the set of all points on the circle between two distinct points on the circle. Specifically, if O is the center of a circle and A and B are points on the circle then minor arc AB is the set of all points on the circle contained in ∠AOB, including A and B. Major arc AB is the set of all points outside of ∠AOB, including A and B. A semicircle is an arc whose "central angle" is a diameter. It's usually defined as the set of all points on a circle that are on one side of a diameter.
In the figure on the right, ∠BDC is a central angle because its center is on the circle. ∠BAC is an inscribed angle because its vertex is on the circle and its sides contain chords of the circle.
is a minor arc because it is contained in ∠BDC. On the other hand, is a major arc because it is outside of central angle ∠BDC.
Arcs are measured in degrees just like angles are. Specifically, the measure of a minor arc is equal to the measure of its central angle. This means the measure of a semicircle must be 180°. Because a circle is made up of two semicircles, there must be 360° in a full circle. This means that the measure of a major arc is 360° minus the measure of its associated minor arc.
