In houses and nature, we often find round objects similar to the shape of a circle. Be it a bangle or a hula hoop that a person uses in their leisure time. They are all in the shape of a circle. In geometry, a circle is defined as a unique type of ellipse whose total eccentricity is zero. Apart from this, the two foci in a circle are coincident.
A circle can also be defined as the locus of the points made at an equidistant from the circle’s centre. To understand the different characteristics and terms of a circle, one must study this shape in detail. The in-depth knowledge of circles can make a person understand terms like radius, diameter, area of the circle, and its circumference.
One can imagine a circle to be a straight line bent to meet both ends. It means if the outline of a circle is detached and made into a straight line, the length of the line and the circumference of the circle will be the same. Let us thoroughly understand the definition, formulas, parts, and some other interesting information related to circles. This information is made regarding meeting the syllabus of competitive exams like NEET and JEE.
What is a circle?
A circle refers to a two-dimensional shape, contrary to the common misconception that it is a three-dimensional figure. The Sun does not have the shape of a circle; rather, it is a sphere. The main difference between a circle and a sphere is that a circle is a two-dimensional shape while a sphere is a 3-dimensional figure.
The round shape of a circle allows it to have a set of all the points in the same plane and equidistant from each other. This point is called the centre of the circle.
Having said this, the shape of a circle is measured in terms of its specific radius. Being a two-dimensional shape, a circle has area and perimeter to explain its different measurable properties. Although we refer to the boundary of any shape as a perimeter, the boundary of a circle is known as circumference. However, the definition of its area remains the same, which is the area encircled around by the circumference of that circle.
The important notes about circles will include the necessary information for the students of class 10th. The aspiring candidates for NEET and JEE can consider these notes for a fundamental understanding of a circle.
What are some daily life examples of the shape circle?
Before proceeding with the different properties and formulas of a circle, it is crucial to understand more about the shape. Understanding the exact shape of a circle will help a person identify and relate to its concepts better.
Some daily life examples that accurately resemble the shape of a circle are-
- Compact disc
- A circular tablet
- Hula hoop
How to draw a circle?
A circle might look like a shape drawn with the best precision. However, drawing it is pretty simple. Besides knowing how to draw a circle, one should also know the measurement and other specifications needed to draw a perfect circle. It isn’t easy to draw a precise shape if a person does not know the measurements, such as the radius of the circle’s diameter.
Following is the stepwise process to exercise the drawing of a circle.
- Take a blank sheet of paper.
- Mark a point somewhere in the centre of that blank sheet as the origin of that circle.
- Now, decide the radius of the circle that you want to draw. It could be 1 cm, 2 cm, 3 cm, and so on. However, it should not exceed the size of the paper.
- Now take a scale and measure the length of the radius from its centre and mark the endpoint of the radius.
- Now, mark as many points as you can at the length of the radius from the centre of the circle. Thus, outlining the circle.
- It is how a circle should look like when you join all the points at the distance of a radius from the centre of the circle.
What do you understand by the centre of a circle?
The circle’s centre is defined as the middle point inside a circle, placed such that it is equidistant from any given point in the circumference. The distance from the circle’s centre to the circumference of the circle is known as the radius.
A circle helps a person understand and identify the different segments of the shape. Apart from this, the circle’s centre is defined as the exact point inside the circle, which is at an equal distance from any given point on the circumference.
What is a semi-circle?
As the name suggests, semi means half. A semi-circle implies the half portion of his circle, which is formed by dividing the whole circle in two. A line segment passing/cutting through the circle’s centre will result in the formation of a semicircle.
The line segment that passes through the centre of the circle, dividing it into two halves, is known as the circle’s diameter.
What is a quarter circle?
A quarter-circle is derived as the one-fourth portion of the circle. A quarter-circle is formed when a circle is divided into four equal portions.
A quarter-circle can also be formed by dividing a semi-circle into two equal parts. That will also resort to the formation of a quarter circle. A quarter-circle is also known as a quadrant.
What are the different parts of a circle?
Although the shape of a circle looks uniform, consisting of nothing but a round shape, there are certain parts and terminologies that a person should know while studying circles.
Following are the components and parts of a circle.
The circumference of a circle is the same as the perimeter of any other shape. It means it is the line that outlines the shape of this circle. The circumference of a circle divides the interior side of the circle from the exterior side.
- The radius of the circle
A radius of a circle is defined as the length from the centre of the circle to any point on the boundary of a circle. The radius is equal no matter which portion of the boundary you choose. A radius is always equidistant from all the points of the circumference of a circle.
- Diameter of the circle
A circle’s diameter is defined as a straight line that passes through the centre of the circle. Thus, dividing it into two halves. A diameter is observed to be twice the size of the circle’s radius. If a line segment does not pass through the circle’s centre, it cannot be a diameter. Apart from this, the diameter is a straight line that touches the circle’s circumference from both sides.
A tangent is a line segment that touches the circle’s circumference at a single point. This particular line lies outside or in the exterior portion of the circle.
- Chord of a circle
A chord of a circle refers to a line segment that touches the boundary or the circumference of the circle at two points. This particular line segment is passed through the circle’s interior for it to touch the boundary twice.
The diameter is the longest chord that passes through the centre of the circle and touches the circumference at two points.
The secant is defined as a line that bisects two points located on the circumference/arc of the circle.
- Arc of a circle
An arc of a circle is a portion of a curve on the circle’s circumference.
A segment of a circle is the area surrounded by the chord of the circle and its corresponding arc. Two types of segments of a circle are- minor segments and major segments.
- The sector of a circle
The area enclosed by the two radii of the circle and their corresponding arc is known as the sector of the circle. There are minor sectors and major sectors in a circle.
Explain the different properties of circles
Now that we have learned about the different parts of a circle, it is time to learn about some fascinating properties. Following are the different properties of circles that set them apart from other geometric shapes.
- A circle is a two-dimensional shape.
- A circle is a curved line. Thus, it has no corners.
- Two circles are congruent if they share the same length of their radius.
- Two equal chords are always at the same distance from the centre of a circle.
- The perpendicular bisector that divides a chord passes through the centre of a circle.
- Tangents drawn at the ends of a diameter are always parallel.
Some important formulas regarding circle
- The formula for the area of a circle:
The area of the circle is given by= π × r × r
r = radius of the circle
- The formula for the circumference of a circle:
The circumference of a circle given by= 2 × π × r
r = the radius of the circle
- Arc length formula:
Length of the arc of a circle = θ x r
- Length of chord formula:
The length of a chord is given by = 2r sin(θ/2)
- Area of segment formula: r² (θ – sinθ) ÷ 2
The shape of a circle helps an individual to understand more about the concepts and studies related to this shape. The above information helps identify the different parts and the related formulas to calculate the different circle parts. The relevant information regarding a circle can help understand the basic concepts of geometry.