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Circles

A circle is a curved plane figure. Every point on the circle is equidistant from a particular point, called the center of the circle. A circle is a 2D shape and is measured in terms of radius. The word ‘Circle’ is derived from the Greek word ' 'kirkos' meaning ‘ring’ or ‘hoop’.

1. What are Circles?
2. Parts of a Circle
3. Properties of Circle
4. Circle Formula
5. Solved Examples on Circles
6. Practice Question on Circles
7. FAQs on Circles

What are Circles?

A circle is a two-dimensional figure formed by a set of points that are at a constant or at a fixed distance (radius) from a fixed point (center) in 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.

What is a Circle?

Parts of a Circle

A circle has mainly the following parts:

Circumference: Circumference of a circle, also referred to as the perimeter of a circle is the distance around the boundary of the circle. 

Radius: Radius is the distance from the center of a circle to any point on the boundary of the circle. A circle has many radii as it is the distance from the center and touch the boundary of the circle at various points

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 points.

Chord: A chord of a circle is any line segment touching the circle at two different points on its boundary.

Tangent in Circles: A tangent of a circle is a line that touches the circle at a unique point.

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

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

Segment: 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: 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.

For better understanding observe the given image depicting all the parts of a circle.

Parts of a Circle

Properties of Circle

Here is a list of properties of a circle.

  • 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 are drawn at the points where the diameter meets the circle is parallel to each other. 
  • Two circles are said to be tangent circles if they touch each other at exactly one point.

Circle Formulas

Let's see the list of important formulae pertaining to any circle.

  • Area of a Circle Formula: The area of a circle refers to the amount of space covered by the circle. The area of a circle totally depends on the length of its radius. Area = π×r2
  • Circumference of a Circle Formula: The circumference of a circle is the whole length of the circle(boundary). Circumference of circle = 2 × π × r
  • Arc Length Formula: An arc is a section (part) of the circumference. Length of an arc = θ × r. Here, θ is in radians.
  • Area of a Sector of a Circle Formula: The sector makes an angle θ (measured in radians) at the center. Area of a sector of a circle = (θ × r2) ÷ 2. Here, θ is in radians.
  • Length of Chord Formula: The length of a chord can be calculated if the angle made by the chord at the center and the value of 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 of a circle = r2(θ − sinθ) ÷ 2. Here, θ is in radians.

Related Articles to Circles

To learn more about the term circle and parts of circle click on the following links.

 

Solved Examples on Circles

  1. Example 1: If the radius of a circular pool is 20 units. What is the length of the diameter of the pool?

    Solution:

    Given: Radius = 20 units ⇒ Diameter of pool (circle) = 2 × r. Therefore, the length of the diameter of circular pool = 2 × 20 = 40 units.

  2. Example 2: John went swimming in a circular swimming pool. After swimming, he runs one round along the boundary of the pool. If the radius of the pool is 35 feet, can you find the distance that John ran around the pool?

    Solution:

    To find the distance that John ran, you need to know the circumference of the circle (pool). For this, you need to know the value of π and r, where r is the radius of the pool. Given: r = 35 feet, π = 22/7. Using the formula, Circumference (C) =2πr ⇒ C = 2 × 22/7 × 35 = 220 feet. Therefore, John ran 220 feet. 

  3.  

    Example 3: You want to decorate your tabletop, which is in the shape of a circle, with a colorful sticker. If the radius of the tabletop is 21 inches, find the amount of paper you need to cover its top surface.

    Solution: 

    Given: r = 21 feet, π = 22/7. Using the formula, Area =πr2, A = 22/7 × 21 × 21 = 1386 square inches. Therefore, the area of a table top is 1386 square inches.

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FAQs on Circles

How Circle is Two-Dimensional?

A circle is a closed two-dimensional figure in which the set of all the points in the plane is at the same distance from the center of the circle. Its real-life examples include wheels, pizzas, orbit, etc.

What are the Formulas of Circles?

Formulas related to Circles are:

  • Diameter of a Circle  ⇒  D = 2 × r
  • Circumference of a Circle  ⇒  C = 2 × π × r
  • Area of a Circle ⇒ A = π × r2

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 The full arc of a semicircle measures 180°.

What is a Chord in a Circle?

A chord is the line segment joining two points inside a circle. As the diameter also having two endpoints in a circle so, it is the longest chord. All angles marked in the circle, subtended by the same chord are equal.

What are the 8 Major Parts of a Circle?

The list of the different parts of a circle is tangent, chord, radius, diameter, minor arc, major arc, minor segment, major segment, minor sector, major sector.

What is the Circumference of a Circle? 

The circumference of a circle is defined as the linear distance around it or we can say, if a circle is opened to form a straight line, then the length of that line will be the circle's circumference.

What are the Properties of Circles?

Following are the properties of circles. 

  • The two circles with equal radius 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.
  • Circles with different radii are similar.
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