Question

The length of the diameter of a circle is how many times the radius of the circle?
A) 1
B) 2
C) 3
D) 4

Answer 1

Hint:
Here, we will find the length of the diameter of a circle in terms of the radius of the circle. By using the property of the circle, we will find the length of the diameter. A circle is a geometrical round shaped figure which has no edges and no vertices.

Complete Step by Step Solution:
We know that in a circle, all points on the circle are equidistant from the origin or the centre of the circle.
The distance between the centre of the circle and any point on the circle is called the radius of the circle. But we know that radius is a constant at all points on the circle.
We know that a chord is a straight line which has its endpoints on the circle. We can draw many chords on the circle by joining two points on the circle.
We also know that the diameter is the longest chord on the circle.

Let \[O\] be the centre of the circle. Let \[P\] be any point on the circle with radius \[r\] and \[AB\] is the longest chord or diameter on the circle.
So, we have \[OP = r\] and \[OP \bot AB\].
By using the properties of chord, we get
Length of \[AB = AO + OB\]
Since all the points on the circle are at equidistant, we get \[OP = AO = OB = r\]
Thus, we get
\[ \Rightarrow \] Length of \[AB = r + r\]
\[ \Rightarrow \] Length of \[AB = 2r\]
Therefore, the length of the diameter is 2 times the radius of the circle.

Thus option (B) is the correct answer.

Note:
A circle is also defined as a curve traced by a point that moves on its plane and is at an equal distance from a given point. Equal chords of a circle are equidistant from the radius of the circle. Equal chords of a circle subtend equal angles at the centre. We used the property that the line segment is drawn perpendicular from the centre, it means both the halves of the chord are equal in length.