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 :

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

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Index

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