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Radius is one of the most important parts of the circle. The radius of a circle is a line drawn from the centre of the circle to its outer edges. Radius can be drawn in any direction from the central point of the circle. In other words, a radius of a circle is a straight line drawn from the centre of a circle to any point on its circumference. A circle An infinite number of radii can be drawn on a circle because there are infinite points on its circumference and all the radii of the circle are equidistant from the centre.

Radius formulas depend on the information that is provided. Here, we will discuss the radius of a circle formula when the circumference, diameter, area of a circle is known.

The diameter of a circle is the straight line passing that starts at one point, passes through the centre, and ends at another point on the circle opposite side. It is also considered the longest possible chord of the circle.

The diameter is twice the length of the radius of a circle. Accordingly, the radius of a circle formula when the diameter is known is derived as:

\[Radius = \sqrt{\frac{Diametre}{2}}\]

The circumference of a circle is defined as its boundary or the length of the once complete arc of a circle. The relationship between and radius and circumference, C, is expressed as C = 2πr. So, when the circumference is known, the radius formula is derived as:

\[Radius = \frac{Circumference}{2 \pi}\]

Here, the value of π is 3.14 or 22/7.

The area of a circle is the number of a square unit that is formed inside the circle. If each square formed in the circle has an area of 1 cm², then you can count the total number of squares to get the area of a circle. Hence, if there are 38,16 total squares, then the area of the circle would be 38.16 cm². However, it is easier to calculate the area using the following formula.

Area = π × radius²

Also, if the area of a circle is given, the radius of a circle formula is given as:

\[Radius = \sqrt{\frac{Area}{\pi}}\]

The radius of a circle that passes through three non-collinear points X₁, X₂, X₃ is given as:

\[r = \frac{|O\vec{X_{1}} - O\vec{X_{3}}|}{2 Sin \theta}\]

Where θ is the angle ∠X₁, X₂, X₃.

The radius of a circle formula with respect to diameter, circumference, and area is given as:

The value of π in the above mention radius formula is 3.16 or 22/7.

Here, we have discussed radius formulas in terms of diameter, area, and circumferences. We have also discussed the radius of the circle formula that passes through the three non-collinear points. It is suggested to understand these formulas as it will help you to calculate the radius of a circle in a fraction of seconds.

FAQ (Frequently Asked Questions)

Q1. What Does the Radius of a Circle Represent?

Ans. The radius of a circle represents the distance from the centre to the edge of a circle.

Q2. If the Radius of a Circle is Doubled, What Effect Does This Have on the Area of a Circle?

Ans. If the radius of a circle is doubled, the area of the circle goes up by 4 times. This is because the area of a circle is directly proportional to the square of the radius of a circle.

Q3. What is the Radius of a Circle with Area X?

Ans. The radius of a circle with area X is given as:

r = √(X/π)