Circle

According to the circle definition, it is a round, closed proportional figure with a Radius, the distance between the centre and any point on the circle. A circle has a fixed and constant radius since all the points on the circle are equidistant from the centre. Circles are used in our day to day lives. Due to its symmetry, it is quite preferred by architects and artists. The word circle is derived from a Greek word whose meaning is ‘ring’ or ‘hoop’. The radius of the circle determines how big the circle will be. The greater the radius, the larger the circle.

Equation of Circle

The basic equation of a circle is given by

(x-h)² + (y-k)²=r²

Where x and y are the coordinates of the circle

And h and k are the x and y coordinates of the centre of the circle, and r here depicts the circle’s radius.

Terms related to Circle

After learning about circle definition, there are certain terminologies one should be familiar with.

• Centre

This is the midpoint of the circle, the distance from which the boundary forms the radius.

• Radius

It is the line segment formed by joining the circle’s centre to any point on the circle.

• Chord

The line segment is formed by joining any two points on the circle.

• Diameter

It is the line segment passing through the centre by joining two points opposite each other. It is the longest chord in the circle.

• Sector

It is the area bound between two radii and an arc of the circle. 

• Segment

It is the region bounded by an arc and a chord formed by two points on the circle. The chord here cannot be the diameter.

• Circumference

It is the total distance covered by completing one full circle rotation.

• Semi-Circle

It is half of the circle. When a circle is divided into half by the diameter, both the parts formed would be a semi-circle.

• Annulus

It is the ring shape formed by two concentric circles. Concentric circles are circles sharing the same centre but having different radii.

• Tangent

A tangent is a line drawn that externally touches the circle only at one point. The radius is drawn from the centre to that point; it forms 90 degrees with the tangent.

Circle Formulas

All the polygons and shapes have their formulas to calculate certain things easily.  The values are put into the formula straight away, and we get the desired result, thus reducing our work. Here are some of the circle formulae.

• Circumference of Circle

Circumference of circle=2πr, where r is the radius.

Where π is pi, but what is pi?

It is constant in maths, whose value can be taken as 22/7 or 3.414  

• Area of Circle

              Area= πr²

• Diameter of Circle

Diameter= 2r

Properties of a circle

After the circle definition, one needs to know about the properties of a circle.

•  The diameter of a circle is the longest chord of the circle.

• Chords of the same length of the same circle subtend equal angles at the centre.

• A circle is a kind of ellipse with eccentricity one and all diameters of equal length.

• The circle is divided into two halves by the diameter.

• Any line drawn perpendicular from the radius to the chord bisects it.

• When the two ends of the chord are joined to the circle’s centre, an isosceles triangle is formed.

• Circles with equal values of radii are congruent.

• If the distance of chords from the circle’s centre is the same, they are equal in length.

• All tangents drawn to the circle are equidistant from the centre.

• Many polygons can be inscribed inside the circle like triangles, rectangles etc.

• A circle can also be inscribed in the triangle, square etc.

• Two circles having different radii would be similar.

Many objects around us are circular. E.g., wheels of the tyres, rings we wear, round glasses, coins, the button in our shirt etc.

Conclusion

As seen from the above information and circle definition, Circle plays a major role in our lives. Most of the objects around us are circular, starting from the vehicle’s wheels to the coins we use as money. The rings and bangles we wear are circular as well. The Cds which we use to play movies are circular as well. It is very different because it doesn’t have any vertices, sides or angles. Its whole figure is completely proportional and symmetrical. After its proper study, its use has increased over time because of its symmetrical nature and better features.