How Many Types of Circle

Introduction

In mathematics or geometry, a circle is a specific kind of ellipse where the eccentricity is zero and the two foci are congruent. The location of points that are equally spaced out from the centre is also referred to as a circle. A circle's radius is calculated by measuring it from the centre to the edge. There are three different kinds of circles: Tangent Circles, Concentric Circles, and Spherical Circles. Circles with varied radii but the same centre are known as concentric circles. Circles with various centres but the same radius are referred to as congruent circles. The circle is the most crucial shape to understand in geometry.

A circle's theoretical significance is used in numerous disciplines, including physics, astronomy, mathematics, etc. In early education, we offer a variety of geometrical shapes to help us grasp other topics where the circle's basic ideas are relevant. A circle is a figure with a circular shape that is used in geometry. We will study what a circle is, and what its diameter, circumference, and other components are in this section. In addition, we will study the different kinds of circles, their characteristics, and their formulas.

Circle Definition

The circle is a curved line that joins at its starting point and is always the same distance from the centre. It is the location of all points that are equally distant from the origin, in other words. Wheels, coins, compact discs, and other objects are instances of circles. The shape of a circle is depicted in the following figure.

Diameter

The diameter is a line segment that runs through the centre and touches both sides of the circle's perimeter. It is the circle's longest chord. Its length is twice as large as its diameter. The symbol for it is d. The diameter is represented in the accompanying figure by the line segment AB. Any straight line segment with ends on the circle that goes through the centre of the circle is referred to as a circle's diameter in geometry. Another name for it is the circle's longest chord. The diameter of a sphere can be calculated using any of the two methods.

A diameter's length, or d, can now be referred to as the diameter. One uses the term "diameter" in this context rather than "diameter," which refers to the line segment itself because all diameters of a circle or sphere have the same length, which is equal to twice the radius "r". The diameter and width of a convex shape in the plane are often described as the maximum and smallest possible distances that can be established between two opposite parallel lines that are tangent to the shape's boundary. The width and diameter of a curve with constant width, like the Reuleaux triangle, may be estimated effectively using spinning callipers. This is because all such pairs of parallel tangent lines have the same distance between them. The terminology is different for an ellipse. Any chord that traverses the ellipse's centre is considered to be its diameter. For instance, conjugate diameters have the characteristic that a tangent line to the ellipse at one diameter's endpoint is parallel.

Formula: \begin{equation}

r=d/2 ,\hspace{0.1cm} d=2r

\end{equation}

Radius

The radius is a section of a line that contacts the centre from one side and the boundary from another. In other words, the radius is the separation between the centre and the circumference. Its diameter is halved in length. By r, it is indicated. The radius is represented in the accompanying figure by the line segment OA. The term "radius" (plural: radii) is used in classical geometry to refer to any line segment that joins an object's centre to its perimeter; in more modern usage, it also denotes the length of those line segments. The plural form of the word "radius" can be either radii (from the Latin plural), or the usual English plural radiuses. The term "radius" is derived from Latin and means "ray" as well as "the spoke of a chariot wheel." The most common abbreviations and names for the mathematical variable radius are R and r. By extension, the diameter D and the radius R are equal.

Circumference

The distance around a circle is its circumference. In other words, a circle's circumference is equal to its arc length. It is the encirclement of the circle. The green dotted line in the accompanying image denotes the circumference. The circumference of a circle is the measurement of its perimeter. The length of the boundary, if the circle is split open and made straight, will equal the circle's circumference. A circle is made up of several points that are evenly spaced out from one another; this single point is referred to as the circle's centre. The distance between any two points along a circle's circumference is known as the radius. The radius is always the same size. It stays the same. The greatest separation possible between any two locations on the circumference is known as a circle's diameter. Its radius is double that.

Origin or Center

The origin is a point at the centre of the circle that is equally spaced from each of its other points. Centre is another name for it. O is the symbol for it. The diameter of a circle is the greatest separation between any two points on the circumference, and in the following diagram, O stands for the origin, or centre, of the circle. Its radius is double.

Tangent

Tangents are line segments that share a common point with the circle. Always, it is drawn outside of the circle. The line segment AB in the accompanying figure is tangent.

Tangency Point

The tangency point refers to the location on a tangent line where it intersects a circle. The line segment AB touches the circle at point P in the accompanying diagram.

Chord

A chord is a segment of a line whose ends are on a circle. Additionally, it splits the circle in half. The line segment AB in the accompanying diagram represents a chord.

Tangent Circle

Two or more circles that have a common centre are referred to as "concentric circles." The radii of these circles vary. The next graphic displays three circles with different radii and the same centre, O.

Concentric Circle

The term "concentric circle" refers to two or more circles with the same centre. These circles have various radii. Three circles with various radii and the same centre, O, are shown in the next image.

Congruent Circle

Congruent circles are two or more circles with the same radii but different centres. Two circles with the same radii but different centres are shown in the next image.

Circle Properties

Some of the circle's crucial characteristics

• Congruent circles are those whose radii are the same.

• The lengthiest chord in a circle is its diameter.

• Two equal portions of a chord are created by dropping a perpendicular from the centre.

• At the location where the radius touches the circle, it is always perpendicular to the tangent.

• On the circle's circumference, angles made by the same arc are always equal.

• An angle created by an arc at its centre is twice as large as the angle it creates when it is inscribed.

Conclusion

The circle is the most crucial shape to understand in geometry. A circle's theoretical significance is used in numerous disciplines, including physics, astronomy, mathematics, etc. In early education, we offer a variety of geometrical shapes to help us grasp other topics where the circle's basic ideas are relevant.