Circles

The term “circle” comes from the Latin word “circulus,” which means “little ring.”  It’s a two-dimensional shape with a radius measurement. A circle is a two-dimensional shape created by a set of points on the plane that are at a definite or constant distance (radius) from a fixed point (center). The fixed point is the origin, or center, of the circle, and the radius is the fixed distance between the points from the origin.

Figure 1:  Parts of circle

Part of circle

These are the part of the circle:

Diameter: A line drawn across a circle going through the center is known as the diameter.

Radius: A radius is the distance between the middle or center of a circle and any point on it. Surprisingly, when two radii are stacked on top of each other, the resultant has the same length as one diameter. As a result, one diameter is twice as long as the radius in question.

Circumference: The circumference of a circle is also known as the perimeter, and it is defined as the distance around the circle’s boundary.

Chord of a circle: Any line segment crossing the circle at two different locations on its perimeter is called a chord. A circle’s diameter is the longest chord, passing through the center and dividing it into two equal sections.

Sector of a circle:  The region contained by two radii and the associated arc in a circle is referred to as the sector of a circle. Sectors are divided into two categories: minor and major.

Arc & Tangent: Tangent is a line that touches the circle slightly as it travels in a different direction. A portion of the circumference, on the other hand, is an Arc.

 Area and Circumference of a Circle

 Area of circle: 

In mathematics, the area of a circle refers to the entire space enclosed by the circle. The perimeter or outline of a circle is referred to as the circumference. In mathematics, there are various methods for calculating the area of circles. The rectangle method can be used to calculate these circle formulas:

Make a circle first.  After that, divide the circle into eight equal halves and arrange them in a rectangle pattern.

The area of the rectangle will now be equal to the area of the square if we calculate it.

Area of a rectangle is = length × breadth

The breadth of the rectangle = radius of the circle (r)

                                              Area of circle = Area of rectangle=122πr×r=πr2

                                                                       Value of is227 or 3.14

Circumference

The circumference of a circle is the length of the circle’s boundary. The circumference of the circle that we drew is the border, as we saw in the section on how to draw a circle. It’s sometimes known as ‘perimeter,’ but that term is more appropriate for forms formed out of straight lines, such as rectangles, squares, and polygons. The circumference of a circle is calculated using the formula C = πd = 2πr, where π = 3.1415.

Properties of circle

The following is a list of circular properties:

• A circle is a two-dimensional closed form that isn’t a polygon. There is only one curved face to it.

• If 2 circles have the same radius, they are said to be congruent.

• Equidistant chords always have the same distance between them and the circle’s center.

• A chord’s perpendicular bisector crosses through the circle’s center.

• The line connecting two circles’ intersecting points will be perpendicular to the line connecting their center points.

• The tangents drawn at the diameter’s endpoints are parallel to each other.

 What is the best way to make a circle?

It’s difficult to draw a flawless circle by hand. A compass (a geometric instrument) is favored when drawing circles in math. The stages of drawing a circle are as follows:

• Take the compass and a ruler first.

• Using the ruler, measure the distance between the tip of the compass point and the attached pencil, depending on the radius (we’ll learn about this in the components of the circle section).

• Next, make a mark in the middle of the paper.

• Place the compass needle’s tip on the point and press it down.

• Rotate the pencil around the point, keeping the needle tip in place, to make a circle.

 Circle Formulas

Circle related formulas given below:

1. Diameter of circle = D=2×r units

2. Circumferences = C=2×π×r units

3. Area= A=r2 

Conclusion

We study,  the circle is the form having the most surface area for a given perimeter length. The circle is a highly symmetric shape: every line through the center has reflection symmetry, and every angle has rotational symmetry around the center. The circle is the form having the most surface area for a given perimeter. The circle is a highly symmetric shape: every line through the center has reflection symmetry, and every angle has rotational symmetry around the centre in this article.