Table of Contents

## Definition of Diameter of a Circle

The **Diameter** of a **Circle** may be defined as the longest chord that passes through the Centre of the circle. For a given circle, an infinite number of** Diameters **can be drawn.

Therefore, for a line segment to be a **Diameter** of a **circle**, the following two conditions must be satisfied:

- The line segment must be a chord of the circle, which means that the starting and the ending point of the line segment must lie on the circle and
- The line must pass through the centre of the circle.

The line segment QOR, represented by the Colour Red in the above figure is called the **Diameter** of the Circle. Both the starting and the ending point of the line QOR lie on the circle and the line passes through the centre O.

The Radius of a Circle is the distance from the centre to any point on the circle. Therefore, the **Diameter** is twice the length of the Radius. The **Diameter of a Circle** can be symbolized by the letter d. It is to be noted that there is an infinite number of **Diameters** present for a given circle. Mathematically,

Diameter = 2 \times Radius

\therefore\,\,\,\,d = 2 \times r

## How to find the Diameter of a Circle from Circumference?

The **Diameter of a Circle** can be found out from the Circumference of the Circle. The formula for finding out the Circumference of a Circle in terms of **Diametre** is given by,

C=\pi \times d

Therefore, the **Diameter** in terms of Circumference will be,

d=\frac{C}{\pi}

## How to find the Diameter of a Circle from Area?

The **Diameter** of a Circle can also be found out from the Area of the Circle. The formula for finding the Area of a circle in from **Diameter** is given by,

A=\frac{\pi\times d^2}{4}

\therefore\,\,\,\,\, d^2=\frac{4A}{\pi}

d=\sqrt{\frac{4A}{\pi}}

d=2\times \sqrt{\frac{A}{\pi}}

## Diameter of a Circle Formulas

The different formulas for finding out the Diameter of a Circle are tabulated below:

Serial No. | Description | Formula |

1 | In terms of Radius | \therefore\,\,\,\,d = 2 \times r |

2 | In terms of Circumference | d=\frac{C}{\pi} |

3 | In Terms of Area | d=2\times \sqrt{\frac{A}{\pi}} |

## Frequently Asked Questions (FAQ)

**1. Define Diameter of a Circle?**

**Answer:** The **Diameter** of a **Circle** may be defined as the longest chord that passes through the Centre of the circle. For a given circle, an infinite number of** **Diameters can be drawn.

**2. How to measure the Diameter of a circle?**

**Answer: **The diameter of a Circle can be found out by using three formulas:

If the radius of the circle is known: d = 2 \times r

If the Circumference of the circle is known: d=\frac{C}{\pi}

If the Area of the circle is known: d=2\times \sqrt{{A}{\pi}}

**3. The Diameter of a Circle is a ____________?**

**Answer: **The Diameter of a Circle is Chord that passes through the Center of the Circle.

**4. How do we find the diameter of a circle?**

**Answer: **The diameter of a Circle can be found out by using three formulas:

If the radius of the circle is known: d = 2 \times r

If the Circumference of the circle is known: d=\frac{C}{\pi}

If the Area of the circle is known: d=2\times \sqrt{{A}{\pi}}

**5. What is the diameter of a circle definition?**

**Answer:** The **Diameter** of a **Circle** may be defined as the longest chord that passes through the Centre of the circle. For a given circle, an infinite number of Diameters can be drawn.

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