The Circle | What is Circle Definition | Features and Formula of Circle
Circle we study of the Circle. Circle is the basic 2D Geometrical plane shape, which has Circumference, Radius. In this chapter we read about Definition of Circle, Circle Circumference, Circle Radius, Diameter of Circle and other different part of circle with Circle important Formula. We also will know about Circle Formula. So let’s start.
The Circle Circle Definition
The set of all those points in the same plane, in which each point is located at a certain distance from a point, called Circle.
Different┬аParts of Circle
A Circle have many parts like Circle Center, Circumference, Radius, Diameter, Chord, Arc, Sector of Circle etc.
Radius of Circle
The distance from the circle center to circumference is called the radius of the circle.
Here OP is a Radius of Circle. We show Radius with r. In a Circle many Radius.
Diameter of Circle
The line segment passing through the center of the circle with its two ends located on the circumference, is called the diameter of the Circle.
Here AB is a diameter of Circle, There are many diameter in a Circle. We show diameter with d.
d = 2r┬а
Center of Circle
A point which distance is equal from the circumference, called Center of Circle.
Here is ‘O’ is the center of a Circle. Which are equal distance from the circumference.
Circumference of Circle
The distance traveled along an entire circle along the circle is called the circumference of the circle.
Here is circumference all around the center of Circle.
Chord of The Circle
The line segment joining any two points on the circle is called the chord of the circle.
Diameter are also a chord and diameter is the largest chord of the Circle.
Arc of Circle
The part of the circle between the two points on the circle circumference is called the arc of the circle.
Here is AXB Short Arc.
and AYB is Long Arc.
Sector of Circle
The area surrounded by an arc formed from two radii and their last points is called the sector of the circle.
Here is AOB is sector of Circle.┬а
Segment of Circle
A part of a circle that is bounded between a chord and an arc is, called Segment of Circle.
Here ACB is short segment.
AYB is long segment.
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Important Formula of Circle
Here Above in Online tutoring class “Tutor Dose” we read about various parts of Circle and their definition. Now we read about Circle Formula.
Area of Circle
Area of Circle = ╬аr2
here r = Radius
(When Radius are given and ask for Area of Circle.)
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Circumference of Circle
Circumference of Circle = 2╬аr
here r = Radius
(When Radius are given and ask for Circumference of Circle.)
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Diameter of Circle
Diameter of Circle = 2r
here r = Radius
(When Radius are given and ask for Diameter of Circle.)
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Radius of Circle
Radius of Circle = \(\displaystyle \frac{{\sqrt{{Area}}}}{\pi }\)
here A = Area of Circle
(When Area are given and ask for Radius of Circle.)
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Radius of Circle
Radius of Circle = \(\displaystyle \frac{C}{{2\pi }}\)
(here C = Circumference of circle)
(When Circumference of Circle is given and ask for Radius.)┬а
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Area bounded by two concentric circles
Area bounded by two concentric circles = \(\displaystyle \pi \left( {r_{1}^{2}-r_{2}^{2}} \right)\)
(where r1 & r2 is radius of both circle)┬а
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Length of Circle Arc
Length of Circle Arc = \(\displaystyle \frac{\theta }{{360{}^\circ }}\times 2\pi r\)
here r = Radius
Theta = Angle on Center of Circle
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Area of Small Sector of Circle
Area of Small Sector of Circle = \(\displaystyle \frac{1}{2}\times {{r}^{2}}\times \theta \)┬а(When radius r and sector of a circle angle are given)
here r = Radius
theta = Angle of Sector┬а
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Area of Sector of a Circle
Area of Sector of a Circle = \(\displaystyle \frac{1}{2}\times L\times r\)
here r = Radius
L = Arc Length
(When radius r and arc length L are given)┬а
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Area of Small Segment
Area of Small Segment = \(\displaystyle \frac{{\pi {{r}^{2}}\theta }}{{360}}-\frac{1}{2}{{r}^{2}}\sin \theta \)
Some Important Questions on Circle
Q.1 A circle diameter is 136 cm, find the area of circle ?
Solution – Diameter of Circle = 136 cm
Radius of Circle = \(\displaystyle \frac{{136}}{2}\) = 68 cm
Area of Circle = \(\displaystyle \pi {{r}^{2}}\)
A = \(\displaystyle \frac{{22}}{7}\times 68\times 68\)
A = 101728/7┬а
A = 14532.57 square cm Answer
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