There are many circular shapes that we encounter in our daily life like coins, bicycle wheels, the dial of a clock, tire, bangles, pizza, etc. Many other objects around us are circular. The term “circle” comes from the Greek word “kirkos,” which means “ring” or “hoop.” There are many Parts of a Circle that make a circle. 

Circles are round, two-dimensional-shaped figures. All points on the circle’s boundary are at an equal distance from a point called the centre. The radius is a line segment connecting the centre of the circle to any point on the circle’s boundary. Continue reading this article to know more about Parts of a Circle.

Definition of Circle

The locus of the set of all points in a plane, which is at equal distances from a fixed point, is called a circle. The circle is a two-dimensional figure. The fixed point of the circle is called the centre of the circle, and the fixed distance is called the radius of the circle.

Objects which are round are called circular objects. There are many such circular objects which we see in our daily life like a disc, basketball ring, tires of a bicycle, bangles, base of the cylinder, the base of the cone, etc.

What are the Parts of a Circle?

Parts of a circle are the terms related to the circle. Some of them are discussed here, which describes the part or portion of the circle.
Centre, radius, diameter, sector, segment, arc, chord, tangent, secant, and circumference, area of a circle are discussed in this article.

Centre, Radius and Diameter of a Circle

The set of locus of all points in a plane, which is at equal distances from a fixed point, is called the circle.

Centre of a Circle

The fixed point of the circle, where all the points are drawn with equal distance, is known as the centre of a circle. From the centre of a circle, all the points on the circle have the same distance. The centre of a circle is the centre point of the circle. In the below-given figure, \(” O” \) is the centre of a circle.

Radius of a Circle

The fixed distance from the point on the circle to the centre of a circle is called the radius of the circle. We can say that the line segment joining the centre to the point on the circle is called the radius of the circle.
The radius of the circle is denoted by \(‘r’\). In the given figure, \(OM\) is the radius of the circle.

Diameter of a Circle

The line segment joining two points on the circle, which passes through the centre of a circle, is called the diameter of the circle. Numerically, the diameter is twice the value of the radius of a circle. A circle can have an infinite number of diameters.

In the above figure, line segment \(MN\) is the diameter of a circle, which passes through the centre \(‘O’\).

Chord, Tangent and Secant of a Circle

Chord

The line segment joining any two points on the circumference of a circle is called the chord of a circle. A circle can have an infinite number of chords. The longest chord of the circle is the diameter of the circle.

In the above figure, the line segment \(QR\) is the chord of a circle.

Tangent of a Circle

A line that touches the circle at only one point is called the tangent of a circle. The point of intersection of a circle with a tangent is called the point of contact.

In the above figure, the line \(QR\) is the tangent drawn to the circle at point \(Q\)
A circle can have an infinite number of tangents, and it can have a maximum of two parallel tangents. At the point of contact, the radius is perpendicular to the tangent of a circle.
From a point on the circle, we can draw only one tangent to the circle, and from an external point, we can draw two tangents to the circle, which are also equal in measures.

Secant of a Circle

A line that intersects a circle at two points is called the secant of a circle. Secant is a line passing through any two points on the circle. In the below figure, the line \(QR\) is the secant passing through the points \(Q,R.\)

Interior and Exterior of a Circle

A circle divides the plane on which it lies into three parts: On the Circle, interior, and exterior.
The portion of the circle, which lies entirely inside the circle, is known as the interior of the circle. The portion of the circle, which is entirely outside the circle, is the exterior of the circle. Any point lying on the circumference of the circle is called ‘on the circle’.

The distance of the point from the centre, which lies inside the circle, is always less than the radius of the circle, and the distance of the point from the centre, which lies outside the circle, is always greater than the radius.

In the above figure, \(O\) is the centre of the circle and the points

1. \(A\) Lies on the circle.
2. \(B\) Interior of the circle.
3. \(C\) Exterior of the circle.

Arc of a Circle

An arc is a connected part of the circle. Arc is a continuous part of the circumference of the circle. Any part of the circumference of a circle is called an arc of the circle.

If the length of the arc of a circle is greater than a semi-circle, it is called the Major arc, and if the length of the arc of a circle is smaller than a semi-circle, it is called a Minor Arc. The sum of lengths of the major arc and the minor arc will always give the circumference of the circle. In the above figure, the part \(MN\) of the circle is known as the arc of a circle.

Sector of a Circle

The region enclosed by two radii and an arc of a circle is called the sector of a circle. Any radius divides the circle into two sectors. The region enclosed by the major arc and radius of the circle is the major sector and, the region formed by the minor arc and the radius of the circle is the minor sector.

Segment of a Circle

The region formed by a chord and an arc of a circle is called a segment of a circle. The segment formed by a major arc and chord is called a major segment, and the region formed by a minor arc and chord is called a minor segment.

Semi Circle

If a circle is divided into two halves, each part is known as a semi-circle. A sector formed with a central angle \(180^\circ \) is called a semi-circle. Semi circle is also known as the segment of a circle, which is formed by the arc and longest chord (diameter) of a circle.

Quadrant of a Circle

One-fourth of the circle or half of the semi-circle is called the quadrant of the circle or quarter circle. A sector with a central angle \(90^\circ \) is called a quadrant. In this quadrant, two radii are perpendicular to each other.

Circumference of a Circle

The perimeter or circumference of the circle is the total length of the boundary of a circle.

The circumference of a circle with radius \(‘r’\) is \(2\pi r.\)

We know that diameter \(\left( d \right) = 2r,\) so, radius \(\left( r \right) = \frac{d}{2}\), then the circumference of a circle in terms of diameter is \(2\pi \left({\frac{d}{2}} \right) = \pi d.\)

Area of a Circle

Space or region enclosed by a circle in a two-dimensional plane is called the area of the circle. The area of the circle with radius \(‘r’\) is given by \(\pi {r^2.}\)

Properties of Parts of a Circle

1. The centre is a fixed point of a circle
2. Radius is a fixed distance from centre to point on the circle.
3. The diameter equals twice the radius, and it is the longest chord.
4. The angle in a circle is \(360^\circ \).
5. The circumference of a circle is \(2\pi r.\)
6. The area of the circle is \(\pi {r^2.}\)

Solved Examples– Parts of a Circle

Q.1. The radius of the circular pool is \(20\) yards. Find the diameter of the pool?
Ans: Given: Radius of the pool \(\left( r \right) = 20\) yards.
We know that diameter of a circle equals twice the radius.
\(d = 2r = 2 \times 20 = 40\,{\text{yards}}\)
Hence, the diameter of the pool is \(40\) yards.

Q.2. Ramu went to a park for jogging. He made one complete round about the park, find the total distance he travelled round the circular park if the radius of the park is \(35\) feet.
Ans: Given the radius of the circular park \(\left( r \right) = 35\) feet.
We know that the total distance travelled around the circular park is known as the circumference of a circle, which is given by \(2\pi r.\)
Total distance travelled \( = 2\times  \frac{{22}}{7} \times 35 = 220\)
Hence, the total distance travelled by a Ramu in one complete round of the circular park is \(220\) feet.

Q.3. Identify the major sector and minor sector of the given figure.

Ans: We know that the region enclosed by two radii and an arc of a circle is called the sector of a circle. It is a part of the circle which is formed by a part of the circumference (arc) and radii of the circle at both endpoints of the arc.
The smaller region is called the minor sector, and the larger region is called the major sector. In the given figure, \(APBA\) is the minor sector, and the region \(AQBPA\) is the major sector.

Q.4. The radius of the circle is \(8\,{\text{cm.}}\) Find the length of the longest chord drawn to the circle.
Ans: Given the radius of the circle \(\left( r \right) = 8\,{\text{cm.}}\)
We know that the longest chord of the circle is the diameter of the circle, whose value is given by \(\left(d \right) = 2r.\)
So, the length of the longest chord is \(2 \times 8 = 16\,{\text{cm.}}\)

Q.5. For the given circle, identify the diameter, chord, tangent, and sectant.

Ans: In the given figure:
1. \(HF – \) Diameter
2. \(BHJ – \) Tangent
3. \(CD,DG-\) chord
4. \(BD -\) secant

Summary

In this article, we studied around the two-dimensional figure, which is known as a circle. The circle is the set of points, which is equidistant from a fixed point and, the fixed point is the centre, and the equal distance is the radius of the circle.
Additionally, we studied the various parts of the circle, such as centre, radius, diameter, chord, tangent, secant, etc. We also discussed arc, sector, segment, semi-circle, quadrant of a circle, circumference, and area of the circle, which helped us understand the problems easily.

Frequently Asked Questions

Q.1. What is the formula for circles?
Ans: The formulas of a circle are
1. Diameter \(\left( d \right) = 2r\)
2. Circumference \(\left(C \right) = 2\pi r\)
3. Area \(\left(A \right) = \pi {r^2}\)

Q.2. What are the two circles having the same centre, and different radii are called?
Ans: Two circles with the same centre and different radii are called concentric circles.

Q.3. What is the measure of the longest chord of a circle when radius \(r\) is given?
Ans: The diameter of the circle is the longest chord of a circle, which equals twice the radius.
Diameter \( = 2 \times {\text{Radius.}}\)

Q.4. What is the sector of a circle?
Ans: Sector of the circle is the region formed by two radii and an arc of a circle.

Q.5. What is the difference between major and minor segments of a circle?
Ans: If the segment of the circle is smaller than a semi-circle, then it is called a minor segment, and if it is larger than a semi-circle, then it is called a major segment. The sum of the area of a minor segment and major segment is equal to the area of a circle.

We hope this detailed article on Parts of a Circle helps you in your preparation. If you get stuck do let us know in the comments section below and we will get back to you at the earliest.