Geometry and Trigonometry

Plane Geometry

Why are arcs and angles important to circles?

Everything starts with the angle whose vertex is at the center of the circle (logically called the central angle of a circle). All the central angles of a circle add up to 360 degrees. Every central angle cuts the circle into two arcs: the minor arc (always less than 180 degrees) and the major arc (always more than 180 degrees). Thus, the measure of the minor arc is actually the measurement of the central angle, while the measurement of the major arc is 360 degrees minus the measure of the central angle. An arc length is the distance between an arc’s endpoints along the path of the circle. Congruent arcs are arcs with the same measurements. When the diameter of a circle separates the circle into two congruent arcs it is called a semicircle.


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