Question

The number of radii that can be drawn on a circle is
$
  (a){\text{ 1}} \\
  (b){\text{ 2}} \\
  (c){\text{ infinite}} \\
  (d){\text{ none}} \\
$

Answer 1

Hint: Radius is the line segment from the center of the circle to the circumference of the circle. So eventually there can be more than 1 line segments that can be drawn. Use this concept to think of the overall number of radii.

Complete Step-by-Step solution:

Let us consider a circle as shown above with center O.
The line joining the center and any point on the circumference is called the radius (r) of the circle as shown in figure.
Now as we know there are an infinite number of such points on the circumference of the circle.
So there are an infinite number of radii which can be drawn on the circle as shown in figure.
So the correct answer is infinite or many (uncountable).
Hence option (C) is correct.

Note: Another definition of radii can be defined as the half the longest chord of a circle. Longest chord of a circle is diameter. A diameter is a line segment passing through the center and whose endpoints lie on the circumference of the circle. So similarly there can be an infinite number of diameters that can be drawn within a circle.