Diameter of a Circle

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:

  1. 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
  2. The line must pass through the centre of the circle.
Diameter of a 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.DescriptionFormula
1In terms of Radius\therefore\,\,\,\,d = 2 \times r
2In terms of Circumferenced=\frac{C}{\pi}
3In Terms of Aread=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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