Center of a Circle

A circle, in particular, is a simple closed curve that splits the plane into two areas: interior and exterior. In common usage, the term "circle" can refer either to the figure's boundary or the entire figure, including its interior; in strict technical everyday language, the circle is only the border, and the entire figure is called a disc. The center of a circle is the point where all the lines that form the boundary meet. The origin of circle is a point from which all distances to it are measured. In this article, we will be exploring origin of circle and its implications.

Center of a Circle

What is the Center of a Circle?

The point inside a circle that is equally spaced from all other points on the circle is considered the center of a circle.

It is a point inside the circle which is at an equal distance from all the points on its circumference.

The center of a circle is often referred to as the origin of a circle.

• A circle's radius-The radius of a circle is the distance between the circle's center and any point on its circumference.

• It is usually represented by the letters 'R' or 'r'.

• A circle's diameter- The diameter is the length of the line passing through the center and touching two points on the circle's boundary.

• A Circle's Chord-A straight line joining two points on the circumference of the circle is the chord of the circle.

• The diameter of a circle is defined as the circle's longest chord.

How to Find the Center of a Circle?

Following is the method to find the origin of a circle by drawing chords.

1. Draw a chord in a circle (ab)

Chord in a Circle

2. Draw another chord parallel to the previous chord (XY)

Another Chord

3. Join points a and y Using a ruler

4. Join points b and x Using a ruler

Join the Points

5. The point where the lines intersect is the center of the circle.

The Lines Intersecting is the Center of the Circle

Solved Example

Example 1: Find the area of a circle whose radius is 28 cm.

Ans: Given,

Radius of circular region = r = 28 cm

Area of a circle = $\pi\,r^2$

= $\dfrac{22}{7}\times 28 \times 28$

= $22\times 4\times21$

= 1848 sq. cm

Therefore, the area of the circular region is 1848 sq. cm.

Example 2: Tell whether the given statement is true or not: If the endpoints of the diameter of the circle are given, then to find the coordinates of the center we use the mid-point formula.

Ans: True, if the endpoints of the circle's diameter are given, then to find the coordinates of the center we use the mid-point formula.

Practice Questions

Q1. Find the diameter of a circle whose radius is 10 cm.

Ans: 20cm

Q2. The radius of a circle is 2 cm. What is the diameter of a circle whose radius is 3 times that of the given circle?

Ans: 12cm

Summary

So, from the article, we know that a circle is made up of all points in the same plane that are equidistant from one another. The center of a circle is the point equidistant from all points on the edge of the circle. It is also the point at which the circle's circumference (the line that defines the edge of the circle) intersects its diameter (the distance across the circle). The center of a circle is important in geometry because it is used to define many other geometric concepts, such as radius, chord, and arc.