In the circle there are two main arcs. They are the minor arc of a circle and the major arc of a circle. The minor arc of circle is nothing but the smallest arc length of the circle whereas the major is the longest arc of circle. The minor arc is nothing but the arc which will be less than the length of the semi circle. Now we see about the minor arc of circle.
The ratio of the angle subtended by the arc of circle can be given as 2p radians or it can be given also as 360 degrees.
minor arc of circle
(Length of minor arc PRQ)/(Circumference) = `theta/(2 pi)`
Length of minor arc PRQ = `theta/(2 pi)` * Circumference = ? * r
Minor arc and the radii of the circle can be called as the sector of the circle. The ratio of the area of sector to total area of the circle is equal to the angle subtended by arc is about 360 degrees.
(Area of the sector PRQ)/ (Area of the circle) = `theta/(2pi)`
Area of the sector PRQ =` theta/(2pi)` * (Area of the circle) = `(theta/2)` * r2.
Problems on Minor Arc of a Circle:
Example 1:
Find the minor arc length of the circle where the angle is 15 degrees and the radius of the circle is 5 cm.
Solution:
The minor arc length of the circle is determined by using the formula as follows,
Length of minor arc = ? * r
= 15 * 5
Length of minor arc = 75 cm
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Example 2:
Find the minor arc length of the circle where the angle is 20 degrees and the radius of the circle is 3 cm.
Solution:
The minor arc length of the circle is determined by using the formula as follows,
Length of minor arc = ? * r
= 20 * 3
Length of minor arc = 60 cm
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