Question

What’s the diameter of a circle? Is it the distance to the middle of the circle or the distance all the way across the circle?

Answer 1

Hint: Here we will understand certain terms of the circle like radius, diameter, circumference and the constant $\pi $. We will establish the relationship between radius, diameter and the circumference of the circle. Now, to determine the answer for the second part of the question we will draw a diagram of the circle with radius r and diameter d and check the line that represents diameter.

Complete step-by-step solution:
Here, we have been asked to describe the term ‘diameter’ of a circle. First let us understand the geometry of the circle.
Now, a circle is a 2 – D geometrical shape in which each and every point on this curve is at the same distance from a fixed point known as the center of the circle. The fixed distance from the center to any point is known as the radius of the circle. Now, twice the radius of a circle is known as the diameter of the circle. So mathematically we have,
$\Rightarrow $ Diameter (d) = 2 $\times $ radius (r)
The length of boundary of the circle is known as its circumference or it can also be referred to as the perimeter of the circle. If we consider the ratio of the circumference and diameter of any circle then it gives a constant $\pi $ whose value is generally taken as 3.14. Therefore mathematically we have,
$\Rightarrow \dfrac{C}{d}=\pi $
Substituting the value of in terms of r we get,
$\begin{align}
  & \Rightarrow \dfrac{C}{2r}=\pi \\
 & \Rightarrow C=2\pi r \\
\end{align}$
Let us draw a diagram of the circle of radius r and diameter which can be shown below: -

Clearly we can see that AB is the diameter and it is the distance all the way across the circle.

Note: Note that the radius is the distance to the middle of the circle so two times this distance will form the diameter which will be all the way across the circle. Remember that the diameter is a straight line and it is the longest chord of a circle. Chord of a circle is a straight line that joins two points on the circumference of the circle.