General Mathematics SS1
Length of arcs of circle.
DEFINITION AND MEANING, LENGTH OF ARCS OF CIRCLE
An arc of a circle is a part of the circumference of the circle.
Hence, an arc is a length or a distance along the circumference of a circle. It is never an area.
A sector is a part or a fraction of a circle bounded by an arc and two radii.
Hence, an arc is a length whereas the sector covers an area of a circle.
The segment of a circle is the part cut off from the circle by a chord. A chord is the line segment AB.
LENGTH OF ARCS OF CIRCLES
If 5 sectors are cut off from 5 different circles and the lengths of the arcs l, radii r and angles measured and compared.
L/2π = /360 or L = /360 x 2 πr = 2 πr /360
hence, in a circle of radius r, the length l of an arc that subtends angle at the center is given by
Find the length of an arc of a circle of radius 5.6cm which subtends an angle of 600 at the center of the circle (Take π = 22/7)
Example 3: An arc of length 12.57cm subtends an angle of 600 at the centre of a circle. Find
(1) The radius of the circle
(ii) The diameter of the circle.
An arc of a circle of diameter 28m subtends an angle of 1080 at the centre of the circle. Find the length of the major arc.
Minor arc angle = 1080
Major arc angle = 3600 – 1080