1. What is the Radius?
The radius of a circle is a line segment that joins the centre of the circle to any point on the circle.
If the centre of a circle is \(O\) and \(A\) is a point on the circle, then:
\(OA = r\)
Every radius in a circle has the same length. This fixed distance defines the entire circle.
2. Radii of a Circle are Equal
A circle can have infinitely many radii, but all of them are equal in length. This equality is what keeps the shape perfectly round.
Example: In circle \(O\), if \(A, B, C\) are points on the circumference, then:
\(OA = OB = OC = r\)
3. Relation Between Radius and Diameter
The diameter is the longest chord of the circle and passes through the centre. It is exactly twice the radius.
3.1. Formula
\(d = 2r\)
This means if you know the radius, you can find the diameter instantly, and vice versa.
3.2. Example
If the radius of a circle is \(7\text{ cm}\), then the diameter is:
\(d = 2r = 2 \times 7 = 14\text{ cm}\)
4. Using Radius in Constructions
When drawing a circle using a compass, the distance between the needle and pencil tip is set equal to the radius. This fixed setting ensures the compass draws a perfect circle.
4.1. Why Radius Remains Constant
The compass keeps the distance \(r\) fixed. As the pencil rotates around the centre point, every point it touches is exactly \(r\) units away from the centre — forming a circle.
5. Radius in Real-Life Examples
Whenever you see circular objects, the radius is the distance from the centre to the boundary — such as:
- The distance from the middle of a clock to its outer edge.
- The distance from the centre of a wheel to its rim.
- The distance from the centre of a round table to its edge.