Parts of Circle
The parts of Circle are Diameter,Radius,Arc and Sector.Relation between diameter and radius
Diameter = 2 x radius
Or radius = r = d / 2.
Circumference ( C ) : The length of a boundary of a circle.
C = 2 Πr
Or C = Π D
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Examples
1) Radius = 4 cm, find the diameter.
Solution :
Diameter = 2 x radius
⇒ Diameter = 2 x 4
⇒ Diameter = 8 cm.
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2) Diameter = 6.4 cm, find the radius.
Solution :
radius = r = d / 2.
⇒ radius = 6.4/2
⇒ radius = 3.2 cm
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2)If the radius of circle is 1.5 cm then find the diameter and the circumference.
Solution :
Diameter = D = 2 r
D = 2 x 1.5
D = 3 cm.
Circumference = C = &pie;D
C = 3.14 x 3
C = 9.42 cm
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Some more parts of circle are as follows:
Arc : A part of a circle between any two points on the circle.
There are two types of arcs 1) Minor arc 2) Major arc.
Here PQR is the minor arc and PR is a major arc.
As arc is a part of a circle so,
Length of a minor arc = Π rθ / 180
Length of major arc = 2Πr - Π rθ / 180
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Examples
1) Find the length of arc of radius 6 cm and angle formed by the two radii is 60 0 .
Solution :
r = 6 cm , θ = 60 0 and Π = 3.14
Length of a minor arc = Π rθ / 180
Length of a minor arc = ( 3.14 x 6 x 60 ) / 180
Length of arc = 6.28 cm
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2) Sector : The region enclosed by two radii and an arc.
Area ( minor sector ) = Πr 2 θ / 360
Area ( major sector) = Πr 2 - Πr 2 θ / 360
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Example : Find the area of sector whose radius is 8 cm , angle θ 30 0 and Π = 3.14.
Solution :
r = 8 cm , θ = 30 0 and Π = 3.14
Area of sector = Πr 2 θ / 360
Area = (3.14 x 8 2 x 30 ) / 360
Area of sector = 16.75 cm 2
Circles
• Circles
• Parts of Circle
• Arc and Chords
• Equal Chords of a Circle
• Arc and Angles
• Cyclic Quadrilaterals
• Tangent to Circle