Minor Arc Major Arc Semicircle

Special names are given to geometric figures that lie on or inside circles. Among these geometric figures are arcs, chords, sectors, and segments.

Arc

The arc of a circle consists of two points on the circle and all of the points on the circumvolve that lie between those two points. Information technology'due south like a segment that was wrapped partway around a circle. An arc is measured not by its length (although it can be, of form) but most often by the mensurate of the angle whose vertex is the center of the circle and whose rays intercept the endpoints of the arc. Hence an arc tin be anywhere from 0 to 360 degrees. Beneath an arc is pictured.

The arc higher up contains points A, B, and all the points betwixt them. But what if the arc went the other fashion around the circle? This brings up an important point. Every pair of endpoints defines two arcs. An arc whose measure is less than 180 degrees is called a minor arc. An arc whose mensurate is greater than 180 degrees is called a major arc. An arc whose measure equals 180 degrees is called a semicircle, since it divides the circle in two. Every pair of endpoints on a circumvolve either defines one minor arc and i major arc, or two semicircles. Only when the endpoints are endpoints of a diameter is the circle divided into semicircles. From this signal on, unless otherwise mentioned, when arcs are discussed you may assume the arc is a pocket-size arc.

Figure %: A major arc, minor arc, and semicircle

A central angle is an bending whose vertex is the middle of a circle. Any central bending intercepts the circle at two points, thus defining an arc. The mensurate of a central angle and the arc it defines are congruent.

Figure %: A fundamental angle and the arc it defines

Chord

A chord is a segment whose endpoints are on a circle. Thus, a diameter is a special chord that includes the middle.

Chords accept a number of interesting properties. Every chord defines an arc whose endpoints are the same every bit those of the chord. For example, a bore and semicircle are a chord and arc that share the same endpoints. The union of a chord with a primal bending forms a triangle whose sides are the chord and the ii radii that lie in the rays that make upwards the angle. This kind of triangle is always an isosceles triangle--nosotros'll define that term in Geometry 2. Also, the diameter perpendicular to a given chord (recollect, in that location is but one such diameter because a diameter must contain the eye) is likewise the perpendicular bisector of that chord. These ideas are illustrated below.

Sectors and Segments

Primal angles and chords also define sure regions within a circumvolve. These regions are called sectors and segments. A sector of a circle is the region enclosed past the cardinal angle of a circle and the circle itself. A segment of a circle is the region enclosed by a chord and the arc that the chord defines. A given segment is always a subregion of the sector divers by the central angle that intersects the circumvolve at the endpoints of the chord that defines the given segment. Sound a little complicated? It isn't. Accept a look at the drawing.

Figure %: A sector and a segment of a circle

The sector is the region shaded in on the left. The rays of the central angle DCE and the arc DE enclose the sector. The segment of the circle, which is shaded in on the correct side of the circle, is bounded past the chord AB and the arc AB. Were the primal angle ACB to be drawn, a sector would be defined that would include all of the segment created by the chord AB.