Circles

A circle is a 2-dimensional closed shape that has a curved side whose ends meet to form a round shape. The word ‘Circle’ is derived from the Latin word 'circulus' which means a small ring. Let us learn more about the circle definition, the circle formulas, and the various parts of a circle with a few circle practice problems on this page.

A circle is a two-dimensional figure formed by a set of points that are at a fixed distance (radius) from a fixed point (center) on the plane. The fixed point is called the origin or center of the circle and the fixed distance of the points from the origin is called the radius. Observe the following figure to see the basic parts of a circle, the center, the radius, and the diameter of a circle.

There are many parts of a circle that we should know to understand its properties. A few important parts of a circle are given below.

Circumference: It is also referred to as the perimeter of a circle and can be defined as the length of the boundary of the circle.

Radius of Circle: Radius is the distance from the center of a circle to any point on its boundary. A circle has an infinite number of radii.

Diameter: A diameter is a straight line passing through the center that connects two points on the boundary of the circle. We should note that there can be multiple diameters in the circle, but they should:

• Pass through the center.
• Be straight lines.
• Touch the boundary of the circle at two distinct points which lie opposite to each other.

Chord of a Circle: A chord is any line segment touching the circle at two different points on its boundary. The longest chord in a circle is its diameter which passes through the center and divides it into two equal parts.

Tangent: A tangent is a line that touches the circle at a unique point and lies outside the circle.

Secant: A line that intersects two points on an arc/circumference of a circle is called the secant.

Arc of a Circle: An arc of a circle is referred to as a curve which is a part or portion of its circumference.

Segment in a Circle: The area enclosed by the chord and the corresponding arc in a circle is called a segment. There are two types of segments - minor segment and major segment.

Sector of a Circle: The sector of a circle is defined as the area enclosed by two radii and the corresponding arc in a circle. There are two types of sectors - minor sector, and major sector.

Observe the figure given below which shows all the important parts of a circle.

Let us move ahead and learn about some interesting properties of circles that make them different from other geometric shapes. Here is a list of properties of a circle:

• A circle is a closed 2D shape that has one curved face.
• Two circles can be called congruent if they have the same radius.
• Equal chords are always equidistant from the center of the circle.
• The perpendicular bisector of a chord passes through the center of the circle.
• When two circles intersect, the line connecting the intersecting points will be perpendicular to the line connecting their center points.
• Tangents drawn at the endpoints of the diameter are parallel to each other.

There are many formulas related to a circle. Let us see the list of a few basic circle formulas pertaining to any circle.

• Area of a Circle Formula: The area of a circle refers to the amount of space covered by the circle. It totally depends on the length of its radius → Area of a circle = πr², where 'r' is the radius and π = 3.14
• Circumference of a Circle Formula: The circumference is the total length of the boundary of a circle → Circumference of a circle = 2πr, where 'r' is the radius and π = 3.14
• Arc Length Formula: An arc is a section (part) of the circumference. Length of an arc = θ × r. Here, θ is in radians, and 'r' is the radius.
• Area of a Sector Formula: If a sector makes an angle θ (measured in radians) at the center, then the area of the sector of a circle = (θ × r²) ÷ 2. Here, θ is in radians.
• Length of Chord Formula: It can be calculated if the angle made by the chord at the center and the value of the radius is known. Length of chord = 2 r sin(θ/2). Here, θ is in radians.
• Area of Segment Formula: The segment of a circle is the region formed by the chord and the corresponding arc covered by the segment. The area of a segment = r²(θ − sinθ) ÷ 2. Here, θ is in radians.

☛ Related Topics

Check these interesting articles related to circles in math.

• Constructing Circles
• Circumference of Circle Calculator
• Equation of Circle Calculator
• Symmetry of Any Circle
• Chords and Diameters

What is the Definition of a Circle in Geometry?

A circle is a curved 2d shape which is obtained by joining those points in a plane that are at the same fixed distance from a fixed point in the same plane. That fixed point is known as the center of the circle. In a circle, the distance from the center to the circumference is termed as the radius and the distance from one point on the circumference to another point passing through the center is termed as the diameter. One of the most common examples of a circle in the real world is a pizza base.

How is a Circle a 2D Shape?

A circle is considered to be a 2d shape because it is flat without any depth and it cannot be physically held. The basic property of a 2D shape is that it does not have any height or depth. A circle has one curved side whose ends meet to make it a closed shape. Its real-life examples include flat surfaces or pictures of wheels, pizzas, orbit, etc.

What are the Circle Formulas?

There are many formulas related to a circle. A few basic circle formulas related to circles are given below:

• Diameter of a Circle ⇒ D = 2 × r, where 'r' is the radius
• Circumference of a circle ⇒ C = 2 × π × r, where 'r' is the radius
• Area of a circle ⇒ A = π × r², where 'r' is the radius

What is a Half-Circle called in Geometry?

In geometry, a semicircle refers to the half of a circle. The diameter divides the circle into two equal parts that are semi-circles.

What is a Chord in a Circle?

A chord is a line segment joining two points on the boundary of the circle. It should be noted that the diameter is the longest chord of a circle because it is a straight line passing through the center that connects two points on the boundary of the circle.

What are the 8 Parts of a Circle?

Although there are many parts of a circle, the 8 main parts of a circle include the radius, diameter, circumference, arc, chord, tangent, segment, and sector.

What is the Circumference of a Circle?

The circumference of a circle is the total length of its boundary. In other words, if a circle is opened to form a straight line, then the length of that line is considered to be the circumference of the circle.

What are the Properties of Circles?

There are many properties of circles. A few basic properties of circles are given below:

• A circle is a 2d shape in which all the points in the plane are equidistant from a point which is called the center of the circle.
• Two circles with equal radii are congruent in nature.
• The diameter is the longest chord of a circle and it divides the circle into two equal parts.
• The radius of the circle bisects the chord if it is drawn perpendicular to the chord.

What are the Types of Circles?

Circles can be categorized into different types, but the 2 main types of circles are:

• Concentric Circles: Concentric circles have different radii but have the same center.
• Congruent circle: Congruent circles have the same radius but have different centers.