Which Parts of a Circle Are Easy to Measure
Parts of a Circle
There are many parts of a circle that make it a circle. A circle is a 2D shape and is measured in terms of its radius. The word 'Circle' is derived from the Greek word 'kirkos' meaning 'ring' or 'hoop'. The parts of a circle include the radius, diameter, circumference, and so on. Let us learn about the circle and its parts in detail.
| 1. | Definition of a Circle |
| 2. | What are the Parts of a Circle? |
| 3. | FAQs on Parts of a Circle |
Definition of 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 two main regions namely, the interior of a circle and the exterior of a circle. The interior of a circle consists of the region inside the circle and the exterior of a circle is the region outside the circle.
What are the Parts of a Circle?
A circle is a closed figure with a curved boundary and has many parts that represent the properties and characteristics of a circle.
Circle and its Parts
The different parts of a circle are listed below:
- 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. In other words, when we measure the boundary or the distance around the circle, that measure is called the circumference and it is expressed in units of length like centimeters, meters, or kilometers. The circumference of a circle has three most important elements namely, the center, the diameter, and the radius.
Since we cannot use the ruler (scale) to measure the distance of this curved figure, we apply a formula that uses the radius, diameter, and the value of Pi (π). The formulas for the circumference of a circle are given as follows:
- When the radius is given: Circumference of a circle formula = 2πr
- When the diameter is given: Circumference of a circle formula = π × D
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 when the circumference is given, we use this formula.
- Radius of Circle = √(Area/π) - 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 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 figure given 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 × √(r2 − d2) (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
The 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 x2 + y2 = a2 for a line y = mx + c is given by the equation y = mx ± a √[1+ m2]
- The tangent to a circle equation x2+ y2 = a2 at (a1, b1) is xa1 + yb1 = a2. This means that the equation of the tangent is expressed as xa1 + yb1 = a2, where a1 and b1 are the coordinates at which the tangent is made.
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 circumference of the circle whereas a secant passes through the circle forming a chord or diameter of the circle.
There are three secant theorems used in the circle which are given below:
- 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 figure given below shows the secant PQ and the chord AB.
Arc of a Circle
The arc of a circle is the curved part or a part of the 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 formula for the area of a segment can be expressed as follows
- Area of a segment of circle = area of the sector - area of the triangle
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.
Sector of a Circle
A sector of a circle is a pie-shaped 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, forming a sector of a circle. The formulas to calculate the sector of the circle are:
- Area of a sector (A) = (θ/360°) × πr2 (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
- Circumference to Diameter
- Semicircle
- 3D shapes
Examples on Parts of Circle
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Example 2: Identify the parts of a circle and state true or false for the following statements:
a.) OS is the radius of the circle.
b.) PQ is the secant of the circle.
c.) If we join O and P, then OP can also be called the radius of the circle.
Solution:
a.) True, OS is the radius of the circle.
b.) False, PQ is not the secant of the circle. It is the chord of the circle.
c.) True, if we join O and P, then OP can also be called the radius of the circle.
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Practice Questions on Parts of Circle
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FAQs on Parts of Circle
What are the Parts of a Circle?
The parts of a circle include the circumference, radius, diameter, chord, tangent, secant, arc, segment, and sector. Each of these parts of a circle plays a significant role in forming a circle.
Which Part of a Circle is the Longest?
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 to be the longest part. It is to be noted that the diameter is 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 - the minor segment and the 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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Source: https://www.cuemath.com/geometry/parts-of-circle/
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