Parts of a Circle: Definition, Parts, Formulas & Examples

Parts of a Circle

A circle is one of the most important shapes in geometry. Students learn about circles early in mathematics because they appear everywhere in daily life. The sun, a coin, a clock, and a wheel are all shaped like a circle. To understand circles properly, students must learn about the parts of a circle, their meanings, and how to use their formulas.

Each part of a circle, such as the radius of a circle, diameter of a circle, circumference of a circle, chord of a circle, arc of a circle, tangent of a circle, secant of a circle, and segment of a circle, has its own definition and purpose.

What is a Circle?

The definition of a circle states that a circle is a closed two-dimensional curve in which every point is at an equal distance from a fixed point. This fixed point is called the center of the circle. The equal distance from the center to any point on the circle is known as the radius of a circle.

A circle does not have corners or sides. It is perfectly round and symmetrical around its center. The boundary line of a circle represents its circumference.

Example of a Circle: The rim of a bicycle wheel, the edge of a coin, or the shape of a clock are good examples of a circle.

Also Read: Unit Circle

What are the Parts of a Circle?

The parts of a circle are the individual elements that describe its structure. Each part has its own definition, formula, and use. The main parts of a circle include the following:

• Center: The fixed point inside the circle which is equidistant from all points on the circle.

• Radius of a Circle: The distance from the center to any point on the circle.

• Diameter of a Circle: The longest chord that passes through the center of the circle.

• Circumference of a Circle: The total length of the boundary of the circle.

• Chord of a Circle: A straight line joining two points on the circle.

• Arc of a Circle: A part or section of the circumference of the circle.

• Tangent of a Circle: A line that touches the circle at exactly one point.

• Secant of a Circle: A line that cuts the circle at two points.

• Segment of a Circle: The area between a chord and the arc connected to it.

These parts together define the full geometry of a circle. Each one is important in solving mathematical problems, proving theorems, and applying circle formulas in practical life.

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Radius of a Circle

The radius of a circle is the distance from the center of the circle to any point on its circumference. It is represented by the letter rrr. The radius is one of the most basic measurements in a circle and is used in almost every circle formula.

Formula for Radius:

 r = d / 2

where r = radius and d = diameter.

The radius is used in many circle-related formulas such as:

• Area = πr²

• Circumference = 2πr

Example: If the diameter of a wheel is 40 cm, then its radius is 40 / 2 = 20 cm.

The radius helps to find the size of the circle and is also used in calculating the length of an arc or the area of a sector.

Circumference of a Circle

The circumference of a circle is the total distance around the circle. It can be compared to the perimeter of polygons. The circumference measures how long the circular boundary is.

Formula of circumference of a circle:

C = 2πr or C = πd

where r = radius and d = diameter.

Example: If the radius of a circle is 7 cm, then C = 2π × 7 = 44 cm (approximately).

The circumference of a circle is used in many real-life applications, such as finding the distance covered by a wheel in one rotation or measuring the border length of circular objects like plates or rings.

Also Read: Perimeter of a Circle

Secant of a Circle

The secant of a circle is a straight line that intersects the circle at two distinct points. It passes through the circle, cutting it into two parts. The part of the secant that lies inside the circle is known as the chord of a circle.

Example: If a straight line cuts a circle at points A and B, then line AB is the chord, and the extended line that passes through these points is the secant.

The secant of a circle is useful in geometry to understand how lines interact with circular shapes.

Arc of a Circle

An arc of a circle is a portion of its circumference between two points. Arcs are curved lines that represent a part of the circle’s boundary.

There are three main types of arcs:

• Minor Arc: The smaller part of the circle between two points.

• Major Arc: The larger part of the circle between two points.

• Semicircular Arc: Exactly half of the circle.

Formula for Arc Length (θ in degrees): 

Arc length = (θ / 360) × 2πr

Example: If the radius of a circle is 10 cm and the central angle is 90°, Arc length = (90 / 360) × 2π × 10 = 15.7 cm (approximately).

Arcs are often used in construction, design, and measurement problems involving parts of circles.

Diameter of a Circle

The diameter of a circle is the longest straight line that can be drawn inside a circle. It passes through the center and touches the circle at two points. The diameter divides the circle into two equal halves.

Formula:

d = 2r

Example: If the radius of a circle is 8 cm, then the diameter is 2 × 8 = 16 cm.

The diameter is used to find the circumference of a circle and the area of a circle using formulas such as C = πd and A = πr². The diameter is also the longest chord in a circle.

Chord of a Circle

A chord of a circle is a line segment that joins any two points on the circle. Every circle has many chords of different lengths. The longest chord is always the diameter.

Example: In a circle with a radius of 6 cm, a line joining two points on the circumference is a chord of a circle.

Chords are important in theorems such as equal chords of a circle are equidistant from the center and perpendicular drawn from the center to a chord bisects it.

Chords are also used to find the area of segments and to study properties of cyclic quadrilaterals.

Tangent of a Circle

A tangent of a circle is a straight line that touches the circle at exactly one point. That point is known as the point of contact.

Properties of Tangent:

1. A tangent is always perpendicular to the radius at the point of contact.

2. Only one tangent can be drawn at a particular point on the circle.

3. A circle can have infinitely many tangents in total.

Example: When a ball touches the ground at one point or when a bicycle wheel touches the road, the line of contact represents a tangent of a circle.

Segment of a Circle

A segment of a circle is the region enclosed between a chord and its corresponding arc. Segments are formed when a chord divides a circle into two parts.

Types of Segments:

• Minor Segment – The smaller region cut off by the chord.

• Major Segment – The larger region cut off by the chord.

Example: If a chord divides a circle into two parts, the smaller region between the chord and the arc is the minor segment, and the larger region is the major segment.

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