Parts of Circle
There are many parts of a circle that make a circle. A circle is a 2D shape and is measured in terms of radius. The word ‘Circle’ is derived from the Greek word ' 'kirkos' meaning ‘ring’ or ‘hoop’. The part of a circle is the radius, diameter, circumference, and so on. Let us learn about these parts in detail.
1.  Definition of a Circle 
2.  What are the Parts of a Circle? 
3.  FAQs on Parts of a Circle 
Definition is a Circle
A circle can be defined as a 2D figure formed by a set of points that are adjacent to each other and are equidistant from a fixed point. The fixed point in this curved plane figure is called the center of the circle, the common distance between the points from the center is called a radius, and a line that crosses from the center of the circle starting from one point to the other is called a diameter. A circle has three main regions namely, the interior of a circle, the exterior of a circle, and on the circle. The Interior of a circle consists of the region inside the circle, the exterior of a circle is the region outside the circle, and on the circle is the region or points on the circle.
What are the Parts of Circle?
A circle is a closed figure with curved boundaries and has many parts that represent the properties and characteristics of a circle. The parts of a circle are:
 Circumference
 Radius
 Diameter
 Chord
 Tangent
 Secant
 Arc
 Segment
 Sector
Let us discuss each of the parts in detail.
Circumference of a Circle
The circumference of a circle is its boundary or the length of the completion of a circle. In other words, when we measure the boundary or the distance around the circle, that measure is called the circumference in units of length like centimeters, meters, or kilometers. The circumference of a circle has three most important elements namely, the center, the diameter, the radius. The center is a point that is at a fixed distance from any other point from the circumference, diameter is the distance across the circle through the center, and the radius is the distance from the center of a circle to any point on the circumference of the circle.
Since we cannot use the scale to measure the distance of this curved figure, we apply a formula that uses both the radius, diameter, and the value of Pi. The circumference formula of a circle are:
 Circumference of a circle formula = 2πr (used when the radius 'r' of the circle and the value of 'pi' is given)
 Circumference of a circle formula = π × D (used when the diameter and the value of pi is given)
 Radius = Circumference/2π (used when the circumference and the value of pi is given)
Where,
 r = radius of the circle.
 D = diameter of the circle.
 π = Pi with the value approximated to 3.14159 or 22/7.
Radius of a Circle
The radius of a circle is the length of the line segment joining the center of the circle to any point on the circumference of the circle. A circle can have many radii (the plural form of radius) and they measure the same. Usually, the radius of a circle is denoted by 'r'.
To calculate the radius of a circle when the diameter, area of a circle, and circumference is known we use the following formulas:
 Radius of Circle = Diameter / 2  The diameter is twice the length of the radius and is also the longest chord of the circle. When the diameter is known, we use this formula.
 Radius of Circle = Circumference / 2π  The circumference is the perimeter of the circle and the radius is the ratio of circumference. Hence, when the circumference is given, we use this formula.
 Radius of Circle = √(Area/π) units  The area of a circle is the space inside the circle. Hence, when the area of the circle is given, we use this formula.
Diameter of a Circle
The diameter of a circle is a line segment that passes through the center of the circle and with endpoints that lie on the circumference of a circle. The diameter is also known as the longest chord of the circle and is twice the length of the radius. The diameter is measured from one end of the circle to a point on the other end of the circle, passing through the center. The diameter is denoted by the letter D. There can be an infinite number of diameters where the length of each diameter of the circle is length.
To calculate the diameter of a circle when the radius, area of a circle, and circumference is known we use the following formulas:
 Diameter = Circumference/π (used when the circumference is given)
 Diameter = Radius × 2 (used when the radius is given)
 Diameter = 2√Area/π (used when the area of the circle is given)
Chord of a Circle
A chord of a circle is a line segment that joins two points on the circumference of the circle. A chord divides the circle into two regions known as the segment of the circle which can be further referred to as minor segment and major segment depending on the area covered by the chord. In a circle, when the chord is extended infinitely on both sides it becomes a secant. In the image below, PQ is represented as the chord of the circle with O as the center.
To calculate the chord of a circle, we use two basic formulas:
 Chord Length = 2 × √(r^{2} − d^{2}) (using perpendicular distance from the center)
 Chord Length = 2 × r × sin(c/2) (using trigonometry)
Where,
 r is the radius of the circle
 c is the angle subtended at the center by the chord
 d is the perpendicular distance from the chord to the circle center.
Tangent of a Circle
A tangent of a circle is defined as a straight line that touches the curve of the circle at only one point and does not enter the circle’s interior. The tangent touches the circle's radius at a right angle. The two main aspects to remember in the tangent is the slope (m) and a point on the line. The general equation or formula of the tangent to a circle is:
 The tangent to a circle equation x^{2 }+ y^{2 }= a^{2 } for a line y = mx + c is given by the equation y = mx ± a √[1+ m^{2}].
 The tangent to a circle equation x^{2}+ y^{2 }= a^{2 }at (\(a_1, b_1)\) is x\(a_1\)+y\(b _1\)= a^{2}
Secant of a Circle
The secant of a circle is the line that cuts across the circle intersecting the circle at two distinct points. The difference between a chord and a secant is that a chord is a line segment whose endpoints are on the curved part of the circle whereas a secant passes through the circle forming a chord or diameter of the circle.
There are secant three theorems used in the circle, they are:
 Theorem 1: When two secants intersect at an exterior point, the product of the one whole secant segment and its external segment is equal to the product of the other whole secant segment and its external segment.
 Theorem 2: Two secants can intersect inside or outside a circle.
 Theorem 3: If a secant and a tangent are drawn to a circle from a common exterior point, then the product of the length of the whole secant segment and its external secant segment is equal to the square of the length of the tangent segment.
The image below shows the secant PQ and the chord AB.
Arc of a Circle
The arc of a circle is the curved part or the part of a circumference of a circle. In other words, the curved portion of an object is mathematically called an arc. The arc of a circle has two arcs namely, minor arc and major arc. To find the measure of these arcs we need to find the length of the arc along with the angle suspended by the arc of any two points. To calculate the length of the arc we use different formulas based on the unit of the central angle (degrees or radians). For a circle, the arc length formula is θ times the radius of a circle. The formulas are:
 Arc Length = θ × r (used for radians)
 Arc Length = θ × (π/180) × r (used for degrees)
Where,
 L = Length of an Arc
 θ = Central angle of Arc
 r = Radius of the circle
Segment of a Circle
A segment of a circle is the region that is bounded by an arc and a chord of the circle. There are two types of segments  minor segment and major segment. A minor segment is made by a minor arc and a major segment is made by a major arc of the circle. To calculate the segment of a circle, we consider the area of the segment which consists of a sector(arc + 2 radii) and a triangle. Hence, the formulas for the area of a segment are:
 Area of a segment of circle = area of the sector  area of the triangle
 Area of minor segment = (θ / 360o) × πr2  (1/2) r2 sin θ (OR) r2 [πθ/360o  sin θ/2], if 'θ' is in degrees
 Area of minor segment = (1/2) × r2θ  (1/2) r2 sin θ (OR) (r2 / 2) [θ  sin θ], if 'θ' is in radians
Note: To find the area of the major segment of a circle, we just subtract the corresponding area of the minor segment from the total area of the circle.
The formula to find the perimeter of the segment of a circle is:
 The perimeter of the segment of a circle = rθ + 2r sin (θ/2), if 'θ' is in radians.
 The perimeter of the segment of a circle = πrθ/180 + 2r sin (θ/2), if 'θ' is in radians.
Sector of a Circle
A sector of a circle is a pieshaped part of a circle made of the arc along with its two radii dividing the circle into a minor sector and a major sector. The larger portion of the circle is called the major sector whereas the smaller portion of the circle is called the minor sector. The 2 radii meet at the part of the circumference of a circle known as an arc, formed a sector of a circle. The formulas to calculate the sector of the circle is:
 Area of a sector (A) = (θ/360°) × πr^{2} (when the angle is given)
 Length of a section (l) = (θπr) /180 (when the length is given)
 Area of a sector of a circle = (l × r)/2 (when the length and radius is given)
 Perimeter of a sector of a circle = 2 Radius + ((θ/360) × 2πr )
Where,
 r = radius of the circle.
 l = length of the arc.
 θ = angle in degrees.
 π = Pi with the value approximated to 3.14159 or 22/7.
Related Topics
Here are a few topics related to the parts of a circle, take a look.
Examples on Parts of Circle

Example 1: The circumference of a wheel is 540 cm. Find its radius and diameter.
Solution:
Given, the Circumference of the wheel = 540 cm.
Circumference of a circle formula = 2πr.
Let the radius of the circle be R.
540 = 2πR
540 = 2 × 22/7 × R
R = 85.9 cm
Diameter = 2R
Diameter = 2 × 85.9.
Therefore, the radius is 85.9cm, and the diameter is 171.8cm. 
Example 2: In the given circle, O is the center, and chord PQ is 20 cm. Find the length of PR if OS is the radius of the circle.
Solution:
We know that the radius of a circle is always perpendicular to the chord and acts as a perpendicular bisector. Therefore, PR = 1/2 × PQ = 20/2 = 10. Therefore, PR = 10 cm.

Example 3: In a pizza slice, if the central angle is 60 degrees and the length of its radius is 4 units, then find the area of the segment formed if we remove the triangle part out of the pizza slice. Use π = 3.142. Round your answer to two decimals.
Solution:
The radius of pizza is, r = 4 units.
The central angle is, θ = 60 degrees.
The area of the segment is,
r^{2} [πθ/360^{o}  sin θ/2]
= 4^{2} [ (3.142 × 60)/360  sin 60/2]
≈ 1.45 square units.
Therefore, the area of the segment of the pizza = 1.45 square units.
FAQs on Parts of Circle
What are the 9 Parts of a Circle?
The 9 parts of a circle are circumference, radius, diameter, chord, tangent, secant, arc, segment, and sector. Each of these parts of a circle plays a significant role in making a circle.
What is the Longest Part of a Circle?
The longest part of the circle is the diameter i.e. the distance from one end of the circle to the other end of the circle. The line segment that passes through the center joining the two points on the circle is considered the longest part. The diameter is also the longest chord of the circle.
What are the 4 Main Parts of a Circle?
The 4 main parts of a circle are radius, diameter, center, and circumference. The center of the circle is the point that is equidistant from all the sides of the circle. The radius is the length of the line from the center of the circle to any point on the curve of the circle. A diameter is a line segment that crosses the center of the circle from one end of the circle to the other end. A circumference of a circle is the boundary or the distance that completes a circle.
How Many Parts is a Segment of a Circle Divided Into?
A segment of a circle is divided into two parts namely minor segment and major segment. The smaller part of the segment of the circle is called the minor segment whereas the larger part of the segment of the circle is called the major segment.
What is the Center of a Circle?
The center of a circle is the point inside the circle that is equidistant from all the points on the curve of the circle. The center of the circle also helps in creating a circle according to any measurement.
What are Secants in a Circle?
The secant of a circle is the line that cuts across the circle intersecting the circle at two distinct points. The difference between a chord and a secant is that a chord is a line segment whose endpoints are on the curved part of the circle whereas a secant passes through the circle forming a chord or diameter of the circle.
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