Terms related to circles

A circle is the shape created by all points in a plane that are at a specified distance from the center, or it is the curve sketched out by a point traveling in a plane so that its distance from a given point is constant. The radius is the distance between any point on the circle and the center. In most cases, the radius must be a positive integer.

Terms related to circles:-

A circle is the locus of a moving point in a plane where the distance between it and a fixed point in the plane is always constant.

The area of the circle is the area of a circle in a two-dimensional plane. The area of a circle can be easily calculated using the formula (A = πr²), where r is the circle’s radius.

The following are terms that are connected to circles:

• Radius

The length of a line that was drawn from the center of a circle to any point on the circle is known as the radius.

• Chord

A chord of a circle is a line segment that connects any two points on that circle.

• Diameter

The diameter of a circle is the length of a chord that passes through its center.

• Circumference

The circumference of a circle is defined as the distance covered by traveling once around the circle’s perimeter or the length of the circle’s border, i.e., the distance covered by traveling once around a circle. 2r is the formula for calculating the circumference of a circle.

• Arc

The term “arc of the circle” refers to a continuous segment of a circle.

• Major arc

A major arc is one that extends beyond the semi-circle length.

• Minor arc

A minor arc is the arc whose length is less than the semi-perimeter of the circle.

• Central Angle

The angle subtended by an arc at the center is known as the central angle.

• Semi-circle

A diameter is the measurement that splits a circle into two equal arcs. A semicircle is made up of these two arcs.

• Segment

The part of the circle that contains the minor arc is known as the minor segment, and the segment that contains the major arc is known as the major segment.

Formula of areas related to circles:-

For the circle of radius r unit,  

1. Circumference of the circle = 2πr
2. Area of the circle = πr²
3. Area of the semi-circle = r22
4. Perimeter of the semi-circle = πr+2r
5. Area of a quadrant of a circle = πr²4
6. Area enclosed by the two circles = πR² – πr² = π (R² – r²) = π (R – r)(R + r)
7. Area of the sector of a circle = 360°× πr²

Value of π:-

Mensuration is a discipline of mathematics concerned with measurement procedures. Measuring is an important aspect of human life. For stitching, we measure the length of the material. A wall’s surface area for painting, or a plot’s perimeter for fencing. In our daily lives, we take numerous different measures of similar items. All of these measurements will be covered in the chapter on mensuration.

π is the most important number when it comes to calculating the surface area and volume of various solid and flat figures. The value of isn’t known with certainty. The tale of how the value was approximated with such precision is fascinating.

The number (pi) is irrational. It can’t be stated as a whole-number ratio.The most used value of π can be stated as 22/7.

Application of these formula:-

Few of the applications of these formula in our real life is as follows:-

• Geometry is frequently employed in engineering and architecture, therefore understanding areas connected to a circle can help us solve real-world problems.
• Sports also make use of areas connected to the circle . These formulas assist in determining many aspects of games such as football, cricket, and others.
• Camera lenses, pizzas, tyres, Ferris wheels, rings, steering wheels, cakes, pies, buttons, and the satellite’s orbit around the Earth are all instances of circles in real life.
• The symmetrical features of a circle are used by architects to design Ferris wheels, buildings, athletic tracks, roundabouts, and other structures.

Conclusion:-

We learnt the definitions of terms connected to circles, as well as the formulas for the areas of a circle, semi-circle, area of a quadrant of a circle, the area contained by two circles, area of a segment of a circle, and area of a sector of a circle, in the preceding article. We’ve also solved several difficulties based on a variety of regions connected to circles and the areas of a combination of planar figures.

The circle is necessary. In short, circular calculations play an important part in everything from building a basic gadget like a clock to developing a complicated nuclear reactor.