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7.8 Lengths of arcs and areas of sectors

An arc is a part of the circumference of the circle; a part proportional to the central angle.

If 3600 corresponds to the full circumference. i.e. 2 p r then for a central angle of x0 (figure 7.24) the corresponding arc length will be l such that

Figure 7.24

Analogically consider the area of a sector. This too is proportional to the central angle. 3600 corresponds to area of the circle p r2. Therefore for a central angle m0 the area of the sector will be in the ratio :

Example 1

In a circle with the radius of 2 cm, the central angle for an arc AB is 750. Find l (seg.AB). Also find the area of the sector AOB having a central angle of 750


l (seg AB) = 2.6



7.1 Introduction
7.2 Lines of circle
7.3 Arcs
7.4 Inscribed angels
7.5 Some properties od tangents, secants and chords
7.6 Chords and their arcs
7.7 Segments of chords secants and tangents
7.8 Lengths of arcs and area of sectors

Chapter 8

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