Parts of a circle (original) (raw)
Last Updated : 9 Feb, 2026
A circle is a set of all points equidistant from a fixed point called the Centre. It is one of the most fundamental shapes in geometry and is widely used in real-life applications like wheels, clocks, and orbits.
Parts of a circle
The parts of a circle include the center, radius, diameter, circumference, chord, arc, sector, segment, and tangent.
Key Components of a Circle
A circle has several important parts and properties that help describe its structure. Here are the main parts of a circle:
Radius
- The Radius (r) is the distance from the center to any point on the circle.
- It is always half of the diameter.
Radius of a Circle
**Formula:
- radius = d / 2 (from Diameter)
- r = \sqrt{(x-h)^2 + (y -k)^2 }
where,
- r = radius
- ( h, k) = Centre of circle
- ( x, y) = any point on the circle
Diameter
- The Diameter (d) of a circle is the longest straight-line segment that passes through its center and touches both sides of the boundary.
- It is denoted by **d and is twice the radius.
- It is the longest chord of the circle.
- It is always twice of radius.
Diameter of a circle
**Formula: The diameter of a circle can be calculated through different methods:
- d = 2 r (from radius)
- d = C / 𝞹 (from circumference)
- d = 2 \sqrt{\frac{A}{\pi }} (from area of circle)
**Real life-examples include: Wheel rotation, pipe flow rate.
Circumference
- The Circumference of the circle is the total distance around its boundary.
- It is the perimeter of the circle and is denoted by C. It plays an important role in geometry, physics, engineering, and real-world applications.
Circumference of a Circle
**Formula:
C = 2 πr (using the radius)
C = πd (using the diameter)
**Real-Life Examples: Measuring circular paths, rotational motion.
Chord
- A Chord is a line segment that connects two points on the circle.
- A circle has an infinite number of chords. The diameter is a chord of the circle.
- A chord divides the circle into two regions the minor segment and the major segment on the area covered by a circle.
Chord of a Circle
**Formula:
chord length = 2\sqrt{r^2-d^2 }
where d is the perpendicular distance from the center to the chord (not the diameter).
Tangent
- A Tangent of a circle is a straight line that touches the curve of the circle at exactly one point. (It does not intersect or enter the interior of the circle).
- It is also known as a non-intersecting line.
- The two important concepts of tangent are slope and point on the line.
Tangent Of a Circle
**Formula:
- For circle (x − h)2 + (y − k)2 = r2, the tangent at (x1, y1) is: (x1 - h) (x - h) + (y1 - k) (y - k) = r2
- For circle x2 + y2 = r2, the tangent at (x1, y1 ) is xx1 + yy1 = r2
Secant
- A Secant of the circle is a 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 a circle.
Secant of a Circle
**Formula:
(length of secant) × (its external segment) = (length of the tangent segment) 2
Arc
- An Arc of a circle is the curved part of a circle or part of the circumference of a circle.
- The curved portion of an object is mathematically known as an arc.
- There are two types of arc namely,
- Minor arc,
- Major arc.
Arc of a Circle
**Formula:
When θ is in radians:
- Arc length = θ × r (used in radians)
When θ\thetaθ is in degrees:
- Arc Length = \frac{\theta}{360} \times 2 \pi r
Sector
- A Sector is pie pie-shaped part of a circle made of an arc along with two radii dividing the circle into major and minor sectors.
- The larger portion is known as Major Sector and the smaller portion is known as the Minor Sector.
Sector of a Circle
**Formula:
Area of Sector=(θ / π360°) x r2 (when the angle is given)
length of Sector=(θ πr❩ / 180 (when the length is given)
Perimeter of Sector= 2 r + ((θ/ 360) x 2 π r)
Solved Example of Parts of a Circles
**Example 1: The radius of circle is 14 meter. Find the area of circle.
Here,
Radius of circle = 14 meterArea of circle = πr2
Area = π(14)2
Area = 3.14 * 196
Area = 615.44 square meter
**Example 2: The circumference of wheel is 600 cm. Find the radius and diameter.
Here,
Circumference of circle = 600 cmFormula for circumference of circle = 2πr
Let us substiute the value of circumference
600 = 2πr
600/2 = 2*3.14*r
300 = 6.28r
r = 300 / 6.28
r = 95.54
Diameter = 2 * Radius
95.54*2
Diameter = 191.08Radius = 95.54
Diameter = 191.08
**Example 3: The diameter of sector is 30 cm, and the angle of sector is 45°. Find the area of the sector.
Here,
Diameter = 30cm and angle = 45 degreeArea of sector=𝛉 / 360 × 2πr2
=45 / 360 × 2 (15)2
=1/ 8 × 2 π(225)
=225 π / 8A ≈ 225 × 3.1416 /8
A ≈ 706.86 / 8
A ≈ 88.36 cm2Therefore, Area of sector is 88.36 cm2
**Example 4: The radius of the arc is 50 cm and the angle substended by the arc is 90 . Find the length of arc.
Here,
Radius of arc= 50 meter
Angle subtend by the arc=90°
Length of arc = 𝛳 / 360 x 2πr
= 90/ 360 x 2π(50)
= 1 /4 x 2 π(50)
= 100π / 4
= 25πLength of arc ≈ 25 × 3.1416 = 78.54 meter
Therefore, Length of arc is 78.54 meter
**Related Articles
Unsolved Question on Parts of a Circle
****Question 1:**The circumference of wheel is 540 cm. Find the radius and diameter.
**Question 2: The radius of circle is 21 meter. Find the area of circle.
**Question 3: The radius of sector is 20 cm. The angle subtended by sector is 90°, find the area of the sector .
**Question 4: A curved road sign is part of a circle with a radius of 6 meters. The arc of the sign subtends an angle of 75° at the center.
****(a)** Find the arc length of the sign.
****(b)** Find the area of the sector representing the curved sign.
**Answer Sheet
- radius = 85.9 , diameter = 171.8
- 1384.74 m2
- 3.1416 m2
- 7.85 m, 23.56 m